Often when I hear Asians speaking English, it is quite easy to tell if it is their first or second language. Their pronunciation of certain words and sounds such as the hard r's and hard and soft t's usually gives it away. So, my question is, is that how we, foreign Mandarin speakers, sound to native Mandarin speakers? I know that Chinese depends a lot on pronouncing the tones of every word correctly. Yet, when I speak Mandarin to my family, they still praise and understand me even though I know that I am getting certain tones wrong. To clarify, do foreign Mandarin speakers sound as bad speaking Mandarin as foreign English speakers do speaking English?
I started this off as a comment but it was getting a bit longwinded so I'll just convert it to an answer.
This question is a bit subjective but I think there is a fair way to look at it.
Foreign Mandarin speakers are easy to sound much worse than most other speakers of second languages.
This is mainly due to what you alluded to in your question: tones. The majority of world languages are atonal - which makes acquisition of a tonal language, especially for adult learners, extremely difficult. If you listen to Korean's speak Mandarin you are very likely to hear tones that haven't even been invented yet in Chinese.
There are also certain initials and finals that some learners seem to perpetually struggle with. 学 /x-ue/ seems to be a particularly big one for Westerners who like to read it: /sh-ui/. Japanese speakers especially struggle with /-an/ at the end of words, often switching it to /-uan/. While most learners are just simply baffled by: /-üe/. And many learners mix up /-o/ and /-ou/.
Most speakers just aren't given the benefit of the doubt. I've seen decent speakers make simple mistakes, that may have been easily overlooked in other languages, met with rapid condescendence. Assuming that the speakers would rather just prefer to speak their native language, i.e.: switching to English; or putting on a "foreign accent" to match the speaker.
Aside from the actual nuts and bolts of the language there are lines of thought that just don't match up. For instance, I've also seen Westerners, person B, have this kind of intercourse:
This kind of non-linear thinking, often trips up native Mandarin speakers and leaves second language speakers sounding even more non-native. One way that could avoid confusion on the above example would be to repeat subject and then ask, "how was it?"
This is all quite ironic because most Mandarin speakers are not first language speakers. The majority of people grew up speaking topolects and dialects as their first language. As a result they can also struggle greatly with speaking "standard" Mandarin, as it is promoted. Using the correct words, getting tones right, pronouncing initials and finals is just as difficult for many of these speakers. And of course, they will say things wrong and cause misunderstandings just like anyone else. But, there is a certain native air to their speaking that earns them the benefit of the doubt.
Two things I want to say about tones.
1, Tones are not as important as they sound if the purpose is to get yourself understood.
You must have been told thousands of times that tones will affect the meaning of the words, and the example given is usually "ma1" (mom) and "ma3" (horse). However, most of the time, the meaning can be told from the context. Actually, I do have a Taiwanese friend referring to her mom as "wo3 de ma3", but we all know what she is talking about. I think that case is much more distinguishable than 四 vs 十 in some dialects. (not Cantonese level "dialect". I consider Cantonese as a different language. The dialect here is something like '河南话' which is not far from Mandarin. However, I was never able to tell 四 from 十 in '河南话'.)
2, Even if you get all the tones right, I will still be able to tell you are a foreigner
The key is the pitch (抑扬顿挫) of sentences, not the tones of characters. Some of my ABC friends speak Chinese very well, which is better than most second language learners. They sound to me like they are speaking perfect Chinese sentences in English pitches.
*, "Do foreign Mandarin speakers sound as bad speaking Mandarin as foreign English speakers do speaking English?"
If you consider it as 'bad', yes they do, but it is 'better' than most dialects sound to Mandarin speakers.
Well, I don't think it is bad as long as understandable.