You’ve touched upon a question about tonal languages that puzzles me.
Using your example. How would a Mandarin speaker get the same effect;
we use tone to distinguish a question from a statement. How would one distinguish “really?” from “really!” in Mandarin?
There are helper words called “particles” that are appended to the sentence to modify its meaning and indicate the mood of the speaker. In this example, “really?” can be translated as “zhen de ma?” (真的嗎?), and “really!” can be translated as “zhen de a!” (真的啊!).
Having said that though, in Cantonese at least, sometimes it’s also ok to indicate a question by raising the tone of the last word in the sentence. I don’t know about Mandarin, or whether this is a modern change in the language due to English influence.
I’m a fumbling beginner in Mandarin, but my Chinese friends can understand me even if I miss or drop tones, though there is still the definite reflexive double-take if multiple meanings can be inferred. Context is key; I may sound like a rube, but I’m not spouting gibberish.
I’ve also noticed that cadence is very important and kills my understandability more than flubbing tones. If you talk…like a…Chinese William…Shatner then you…will definitely have…problems.
From my limited attempts at Mandarin, China Guy has explained why tones are so difficult for “nontonal” language speaker. It’s not that we don’t hear them, it’s that we use them for an essentially grammatical function. Thus, if you just had a nontonal language speaker read something from a transcription, there’d be a strong impulse to put in the wrong tones to indicate starts and ends of phrases, questions, and so on. I don’t know if wrong tones would be worse for the Mandarin speaker than no tones at all, but it certainly would be different.
‘laoshu’ is mouse.
For some people, it’s easier to blame the exotic oriental tones than admit that they just suck at picking up vocabulary.
Mouse is LaoSHU, Teacher is LaoSHI
EDIT: Oops… already corrected.
Well I don’t know why. That’s a perfectly obvious truth.
Helix1047 - I can’t parse what could possibly have been said to go from “self study is slow” to “sleeping along is dull.” come back and help us out.
自学很慢 - zixuehenman = self study is slow
自睡很? - zishui hen ??? = sleeping alone is ???
xue and shui may sound similar to an untrained ear, but the issue is not a tonal one.
Here’s an example my kids had yesterday.
睡袋 = shui4dai4 is sleeping bag
水袋 = shui3dai4 is a water bag (eg something like a boda bag), although normally you would say hot water bottle.
谁带= shui2dai4 is who brings?
There are probably a few other combinations using shuidai in various tones. But it was obvious from the context alone that they had to be talking about a sleeping bag.
Here’s a really good example that I learned my first month of Chinese in University.
请问 = qing3wen4
请吻 = qing3wen3
Two words that have the same pronunciation, same first character but the second syllable has a different tone and character.
The first example is literally “please question” aka “question please” or “may I ask a question”
The second example is literally “please kiss” aka “kiss please” or “may I have a kiss”
My Chinese professor asked “if I was sure” and then she gave me a quick chaste peck on the cheek. (this would probably be considered sexual harrassment these days. That said, she was a 50+ married mother of two boys about my age at the time and the nicest person in the whole world.)
It did highlight the importance of tones, and I have always made sure to get the tones correct on these two instances. However, it really is case by case and context. Sometimes a tone is critical, but most of the time it’s not a deal breaker. YMMV
My guess is 自睡很悶 - zi shui hen men.
Another good example is the difference between “to buy” 買 (mai3) and “to sell” 賣 (mai4). However, unless you’re a stock trader, hopefully the intended meaning should be obvious based on context.
Then this would be a case of butchered pronunciation (not butchered tones)
and if you are a stock trader, then one says ‘mai3jin4’ to but and ‘mai4chu1’ to sell.
Interesting. The Chinese “on” reading of both these characters in Japanese is “bai” (which, helpfully or not, sounds just like English “buy”). Actually the “sell” character is written 売 in Japanese, but I guess you posted the simplified character.
Back on topic, there have been many examples posted here where ambiguity could result from incorrect or unclear tones. But these examples, taken out of context, don’t prove anything about how much would be understood without tones.
What about pinyin, written without tone markings? Or spoken Mandarin rendered by Stephen Hawking’s DECTalk synthesiser?
Actually, those are the traditional characters (買 and 賣). The simplified characters are 买 (to buy) and 卖 (to sell). I think they look butt ugly. 
My contention is that, if we are talking about a complete and realistic conversation and not just some isolated snippets devoid of any context, while there may be some occasional ambiguities, they shouldn’t happen often enough to be a major impediment to understanding.
I’d venture to guess that it’s the Japanese character that’s been simplified; and it’s not the same “simplified” character as they use in mainland China, which is 卖 .
You are right; the Japanese character has been simplified. ISTR you can see the traditional version on the print edition of the Yomiuri newspaper, where the name of the paper appears on the front page masthead something like this: 讀賣.
Apologies again for the hijack.