Most linguist would say at least 21 vowels in English.
Yes, and in addition to the various and apparently unrelated meanings of the same phrasal, the syntax (separable vs. inseparable; transitive or intransitive) adds another layer of difficulty.
And while spoken production of language in which native speakers would normally opt for phrasal verbs can usually draw upon other (usually latinate) verbs of equivalent meaning, the difficulty arises in listening (and to a lessor degree reading) natural discourse. So the English learner would have no problem calling attention to something by saying, “Look at this,” hearing someone say, “Check it out,” in rapid natural speech is more difficult to process.
Really, competency with these verbs is something that is truly acquired only by extensive exposure to the language, especially in spoken contexts.
I’m surprised more hasn’t been said here about English spelling, which is very irregular - bad enough that it’s common for well-educated native English speakers to be bad spellers.
I know a native Russian speaker who has been in this country for over four years and still has trouble with articles. Russian doesn’t have any.
One of the things that I have noticed that French, German and Swedish* speakers have a problem with is the use of ‘since’ and ‘for’ when describing a period of time. It would be common to hear phrases such as “I have been working on this since three months” rather than “I have been working on this for three months” or “I have been working on this since April”. I presumed that their native languages lack such a distinction, though I never bothered to ask them.
Another term which seemed to phase French speakers was “software”. They would refer to a piece of software as “a software” and several programs as “some softwares”, yet never seemed to be confused by the conventional usage by native English speakers.
*and probably others foreign speakers also, but I used to work with these nationalities so picked them up
I work with francophone programmers and see this all the time. English uses articles that are skipped in French: “Word est un logiciel” = “Word is a *piece of *software”, “Il est artiste” = “He is *an *artist”. To make things trickier, it’s not consistent so it’s harder to explain: “Je vais chercher un café” can be rendered as either “I’m going to get a cup of coffee” or “I’m going to get a coffee”.
That was one of the hard things in the beginning: after getting speech training in kindergarten to get rid of the lisp, now I had to learn to lisp again, but only with “th”, because English still has regular “s”, too!
The question of whether sounds are more difficult to make or spelling correctly depends on whether you are thinking of people learning to speak English or to write English. (Yes, in the end, people need both skills to master English - but in the beginning, talking and understanding spoken English is going to be more difficult than reading and writing, I think. There’s also the disparity between active and passive vocabulary, so reading words in English will be easier to understand than hearing them, or using them activly.)
Another one I thought of: the use of auxiliary verbs in the negative. Can not is not the opposite of can; must not is not the opposite of must, but means you are forbidden to do…; I still get confused about those.
I don’t know why you would think this. But the “since/for” distinction plays a role along with the “ing” form, which these languages don’t have. We know and can express the difference between “I’ve been working for three months” and “I’ve been working since three months”, but use different grammar to express it. (Ich habe drei Monate lang gearbeitet / Ich arbeite seit drei Monaten). My english teacher used the trick of saying that the dot on the i of since meant that a point in time was referred to, to help us seperate when to use “since” and when “for”.
However, the general problem with all those rules, even the ones with tricks to remember them, is that when you’re talking normally, you don’t have the time and brain capacity to consider 20 or more different rules and their exceptions and apply them. I knew the rule about 3 person-s on verbs, but when talking, I still got mixed up because I was too busy thinking about the words themselves, the order and the other problems.
If you get beyond the beginners and intermediate level and reach advanced, close to like a native, you stop thinking in your own language and start thinking in the foreign language, and you stop thinking about rules, but do things by feel, just like you do in your native language. But to reach that stage, you must read and listen and talk a lot. And then you loose it quickly if you can’t practice. 
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Another term which seemed to phase French speakers was “software”. They would refer to a piece of software as “a software” and several programs as “some softwares”, yet never seemed to be confused by the conventional usage by native English speakers.
Well, those words were plural is the same as singular, or the words that don’t really have a plural or singular are different in each language, so they have to be learned by rote. If you forget that software is irregular, you add a plural -s when talking about two pieces of software.
“You bought it off that girl with the great knockers ?.”
“Yeah, the one who was knocked up”
It really does depend on the ESL speaker’s native tongue.
My main experience is with Polish people - many of my relatives live in Poland, and some of them have learned the rudiments of English while others are fluent, so I’ve seen how the progession goes.
For them, the hardest things are the aspects that don’t exist in Polish, naturally. The r/l issues of some Asians, for example, aren’t an issue for Poles because their alphabet contains an “R” and an “L.” But the sound “th” does NOT exist in their language at all, and so if they need to say “Tom Thumb,” it comes out as “Tom-Tum.” (And they need to say it if they move to North Dallas or come visit, because it’s the name of a grocery chain around here. So I’ve heard “Tom-Tum” a lot! :p)
I think articles top the list for a lot of people - the Polish language simply contains no equivalent for “the” or “a/an” and the differences aren’t always cut & dried. But if you use the wrong one it really sticks out to native speakers.
One thing others haven’t mentioned yet (I think?) is the English tendency to slur letters into one another, and how vowels tend to blur towards a generic sound (linguists show it with an upside-down “e”).
The top example is the word “butter.” There’s a slurry sound to it that ESL students just can’t get, because they try to get it right and the only way to make it sound good is to NOT try. (I know, right?) The ESL crowd will enunciate the “t” sound, or the “r” at the end, and that gives it away.
In fact, not only is “butter” my personal shibboleth when I’m outside the US, it is also the word that defines the word shibboleth in my mental vocab lists. ("What’s that word again? Oh, yeah - it means the thing I do with the word “butter.”)
It isn’t? 
Another couple of examples:
Say I’m sitting in a chair, and there is only one empty chair in the room. A friend walks in, and I tell him, “Have a seat,” even though I’m referring to a specific chair: the only one available.
If I’m visiting an unfamiliar house, I might ask the host “Where’s the bathroom?” even though I don’t particularly care which bathroom I use.
I used to teach remedial English in college, and many of my students were second- or third-language learners. I wouldn’t swear it was the biggest problem, but articles seemed toughest on my Asian students.
“An” or “a” can usually be exchanged with “one,” whereas “the” can’t.
There’s one apple in the bowl, next to the banana - works and keeps the same meaning as with “an”.
One apple of the Zambian apple tree is unusually sweet - gramatically correct but it doesn’t have the same meaning as with “the.” With “The,” it means “any and all the apples of that kind of apple tree;” with “one” it’s a single apple out of all the apples ever produced by that whole family of trees.
Hispanics usually have a horrid time with some phonemes (the “th” family, the j) and with verbs. Y’all need better subjunctives! And a plural for “you” 
Countables vs uncountables (much vs many) is a pain as well, but I’ve seen natives have serious problems with it.
Idioms are difficult, but that’s true of any language, it’s not a peculiarity of English. Idioms in your own language sometimes make little sense, so imagine in a different one (add being about something that doesn’t exist in your culture/times and a fondness for idioms becomes a recipe for disaster).
Maybe a useful way to think about “a” vs. “the” is that “the” refers to something that is unique, in the context that you are referring to. Either because you have referred to it already (“I saw an apple, and I picked the apple up”), or because it goes without saying that it is unique (“the President of the United States”).
In my example, “the apple of the Zambian apple tree” refers to a unique type of apple, not a unique instance of apples in general, so the rule does in fact hold. In my counterexample “there is an apple in the bowl”, it is talking about one apple, but the apple hasn’t been mentioned before and the context is of all the apples in existence. You could refer to the same apple as “the apple in the bowl”, because then the context is only of apples in that bowl, and there is only one such apple.
No doubt somebody will be able to sink this theory with another counterexample 
‘Unique in context’ is the phrase I use too.
Of course, that’s for common nouns, not names of places and so on.
That’s probably a carry-over from older times. Nowadays, most houses have multiple bathrooms, but a few decades ago, it was the norm for them to only have one each. If someone visits my mom, and asks for “the bathroom”, they’re interested in the one singular specific room with a toilet in her house.
Yes, spoken language is natural; it exists a priori to writing—the human animal, under normal circumstances, will learn to speak at least one language more or less effortlessly. Writing is an artifice—it’s taught primarily as a means of communicating without speech, which is temporal, and the manner in which it’s transcribed is subject to all kinds of artificial intervention.
All too often people think of a language solely (or primarily) in its written representation, as though the written representation were its origin, and this unfortunately often happens in English language instruction. One of the most common and lamentable errors in basic ESL/EFL instruction is to introduce new language in print before speech.
Yes. It’s not about use of since, rather, in this case, whether one is referring to habitual activity or momentary activity.
But this isn’t correct—that is, it’s not correct usage. It’s clearly a stative expression (like own, possess, etc.), and should be expressed with a simple present verb. Just because a form is conceivably correct grammatically, doesn’t mean it’s correct pragmatically. Generally with have it’s idiomatic expressions that will take on progressive aspect (e.g., Are you having a good time now?)
Not necessarily. This assumes that the learner is already familiar with the vocabulary. And hearing is just as passive as reading.
Even native speakers (of American English) have difficulty distinguish between can and can’t; how many times have you had to ask for clarification (“Did you say ‘can’ or ‘can’t’???”). (The difference, which is obviously even more difficult for learners to hear, is that can usually isn’t stressed, while can’t is somewhat. That the terminal /t/ isn’t released doesn’t help.
And pariphrastic not have to is very much not the “opposite” of have to.
You mean the schwa (/ə/), which is the most common form of vowel reduction in English (or “slurring,” as you say). However, the first vowel in butter is not reduced; it’s not a schwa, but rather the stressed equivalent of the schwa (/ʌ/).
In British English, a medial /t/ is usually pronounced as the underlying phoneme; it’s in American English where it becomes the flap or tap (/ɾ/ as in butter), a glottal (/Ɂ/ as in bottle), or simply “null,” as in center. If they don’t employ these sounds (or lack thereof) it’s not necessarily wrong, but in the States it’s incumbent upon the teacher to explain this phonology in a understandable way. As for the r-coloring in butter, it might help to present this sound, which most Americans employ, as a vowel unto itself (/ɚ/).
I don’t know that I’d call the natural changes of language usage “laziness” or “ignorance.” Is a tree lazy because it bends with the wind?
Yeah, 56 rules is about as helpful as no rules.
Because over the centuries, with the various invasions of England by foreign powers, the pronunciations changed as these foreigners tried to communicate with the natives. Few people could write, and those that could (mostly clergy), didn’t change the spellings. There never was an “official” academy to dictate new spelling.
I presented on this once at UCLA. It seems it’s a question of understanding the agency of the verb (i.e., Who bores?) If the learner hasn’t grasped this, the errors are likely to continue.
Well, you have to admit that that’s a pretty vague way of putting it. And immersion in an English-speaking culture is, in a way, osmosis.
Not to mention that many nouns are sometimes count and sometimes non-count depending on the meaning one wants to convey.
In informal speech we do have a plural for you–actually, at least two: you guys (sometimes shortened to simply guys), and you all (y’all).
Or “you’uns” (short for “you ones”, and pronounced, roughly, “yinz”) in the northern Appalachians.
British RP has the advantage of two completely different pronunciations for can and can’t (a as in hat and a as in car). However, since one of the commonest pronunciation difficulties presented by EFL learners is that they say short vowels instead of long ones, I make sure they really know how to say can’t with a long vowel.
I don’t really want them saying ‘you can’t’ to someone who might take it badly if said with a short vowel. 
This, and non-English speakers, and most English speakers, should note it *once was *WORSE. (I almost said “used to be,” but realized that would probably be extra confusing for our lurkers.) Trade languages are simpler than their originals but, in the case of English, that ain’t saying much.