I guess technically this has nothing to do with nicknames, but non-Chinese people mispronounce 'Beijing' and 'Shanghai', which are not hard to pronounce (even for a white American like me), literally 100% of the time.
Ok class, say it with me:
Beijing = "Bay JING", with a hard 'J' (Everyone says Bay 'zhing'.. I'm not sure where that 'zh' pronunciation even came from, because that sound is fairly rare in both English and Chinese)
Shanghai = "SHONG Hai"; both of the 'a's in Shanghai are long 'a's, and should be pronounced like the 'a' in 'car' or 'far' or 'Hahvahd yahd'
There are certainly some hard-to-pronounce city names out there, but Beijing and Shanghai certainly aren't in that category, and considering they are two of the world's most important cities, we might as well pronounce them right
Also: I'm sure someone has already pointed this one out here, but people in Montreal are (in my experience) annoyed when they hear 'MON'treal.. The 'Mon' in Montreal is like the 'Mon' in Monday, and pronouncing it MON is a complete dead giveaway that you're an out-of-towner.