On a college campus, this can be a major problem. Even if the speaker speaks English fairly well, an accent can cause problems.
This occurred to me while listening to a 3 hour lecture from an instructor that someone else claimed to not have been able to understand. I see 4 very broad possibilities why I could understand him while my associate could not.
1) I can hear better than my associate. Not very likely.
2) I've spent more time around foreigners and immigrants of various language backgrounds (including watching lots of British sitcoms) and I've become fairly decent at filling in the blanks and determining what the speaker means to say. In one class, our Nigerian professor had me translate the somewhat rough English of the Indian students into language he could understand!
3) I read a lot more than my associate. Therefore, I have a better command of the English language (although that's not always obvious from reading this blog!) and I can figure out what other people, especially foreigners or immigrants, are trying to say. Or
4) My associate is from east Texas and well, let's just say Jeff Foxworthy would occasionally need a translator here!
I'm sure someone has done some research on whether reading is correlated with the ability to understand what those with accents or who speak in broken English are trying to communicate. It'd interesting to see.
One more fun thing about many immigrants and foreigners is that they don't initially realize what is and what is not appropriate casual conversation in America, therefore they will occasionally say something to you that would result in an American being punched!