I disagree with that website. People always refer to “the arts”, and some people have had many loves. Also, cow’s milk and goat’s milk are not two different milks; they’re two different types of milk. Saying “two different milks” is just sloppy English shorthand. 
Unless they play hockey.
Hey, Chefguy, when you go through the lunch line, would you grab a couple of hamburgers for me and my buddy? Oh, and also, a couple of milks?
When people refer to “the arts”, they are very explicitly referring to different categories/classifications of art (painting, sculpting, dancing, etc).
Of course, when they’re referring to the products of those artistic endeavors, it’s back to being uncountable again. “Go unload the arts from the truck; the auction is starting soon.”
I am partial towards this one that I made up:
pet peef → pet peeves.
John Allen Paulos (author of Innumeracy) suggested that the plural of spouse is spice.
(And is rice the plural of rouse?)
The distinction between discrete vs collective nouns is a bit idiomatic, as different languages have different choices of which nouns are which. For example, “water” is a collective (uncountable) noun. Yet we see Biblical-sounding constructions like:
This comes directly from the Hebrew, where “water” is used that way. We do similarly in English with the word “sky” (e.g., “Clear skies are forecast”).
Another source of odd plurals in English stems from the fact that English is an amalgam of many other languages, and borrowed words often retain their plurals from the source language. German plurals (-en) and French plurals (e.g., -aux) are well-known enough in English. But you also have “cherub” → “cherubim” which is the perfectly standard form of Hebrew masculine plural.
Another way to express plurals is through the use of classifiers. They are standard in some languages like Indonesian (though they tend to be dropped except in formal language) but not all that common in English. Probably the best known examples are head and sheet:
Six head of cattle
Three sheets of paper
Peculiar sounding plurals like the milk example from @Left_Hand_of_Dorkness can be solved by use of a classifier - probably what you’d say is “a couple of cartons of milk” rather than “a couple of milks.”
I note that there’s a little inconsistency in my examples above - why is it “head” singular but “sheets” plural? I’m sure there is an explanation but I don’t know what it is.
Interesting–for me, “a couple milks” would be a completely normal way to express the idea that you express with “cartons of milk.” If I’m going on a field trip and kids pick up lunches in the cafeteria before we go, I’d tell the class, “Put your lunches beside you on the seat, but put your milks in this cooler,” without thinking twice.
And if someone told me that they stay away from non-dairy milks because they all taste nasty, it wouldn’t occur to me that “milks” would be nonstandard there.
(When I Google “a couple milks,” one of the links is to “Download premium image of Romantic lesbian couple”. Maybe I need to be careful about my search history.)
I personally insist that the plural of “mouse”, when referring to the rodent, is “mice”, but the plural of “mouse”, when referring to the pointing device, is “mouses”.
A certain well-known character in the genre of children’s entertainment would argue that the plural of “mouse” is “meeces” (although the correct spelling may not be well-defined).
Princes + s = Princess?
That’s the one I came up with first. Looking at a list, I found another common one and an uncommon one before I got bored. The other common one involves two words which are also verbs.
Here’s a pretty decent link about confusing count/uncount nouns.
I’m curious if any of these examples sound odd to people who would object to “two milks.”
Left_Hand_of_Dorkness’s example sounds perfectly natural to my ears. Like if I have a fridge with a bunch of single serving milks for the kids, it wouldn’t sound at all strange for me to say “hey, honey, can you grab me a coke and a couple of milks for the kids?”
I’ve always enjoyed it when McMansionHell.com refers to “an art” in reference to some random wall hanging in a picture from a real estate listing.
This is the sort of post that I simply want to upvote.
Some comedian suggested that since the plural of ox is oxen, the plural of box should be boxen.
I thing the weirdest plural in English is cavities. The singular word is cavies 
???
bras + s = brass?
This points out a peculiarity of English (and some other languages), that nouns can be used as adjectives to modify other nouns, such as “chicken soup” or “chicken burrito”. This is called an “adjunct noun” or other similar terms. This can lead to ambiguities such as “huge garage sale” (is this a huge sale of garages, or a sale of huge garages?)
In Spanish, to the best of my knowledge, this construct doesn’t exist, and so this kind of ambiguity does not exist. You cannot properly ask for a “chicken burrito”, but must ask for a “burrito of chicken” (burrito de pollo). Of course, “pollo burrito” is often used, but that is strictly Spanglish, AFAIK.
In Hebrew, this is a perfectly standard construct, and in fact there is a specific case for it. Oddly, though, when a noun is used as an adjective, it is the noun being modified that is inflected, and not the noun doing the modifying. This construction is commonly used also to create the possessive case.
That reminds me of an essay James Thurber wrote on “The container for the thing contained.” It was prompted by a story someone related to him, which ended “I threw the milk at him.”
Of course, what she threw was a container of milk, and Thurber was tempted to correct her, but then he realized that this was a common usage, not just for milk, but for other things too. He couldn’t find it in any of his usage handbooks, though, so he dubbed it “The container for the thing contained.”
There was a popular mainframe-class computer in days of yore called a VAX, built by Digital Equipment Corporation. Among the computerati, the commonly used plural was “Vaxen”. And the various varieties of Unix systems were called “Unices”.
(ETA: And I suppose the many varieties of Linux would be called Linuces, although I don’t recall that I ever actually saw that attested.)
There’s an old style of using the singular for amounts, such as “That place is a good 10 mile down the road”. I know someone who talks that way, it’s odd, you might think it was a slip the first time, but you catch on after a while.