Yeah I remember I had a math teacher who had a real thick accent so it was difficult to understand what he was talking about. Accents in general I don't have a problem with, but when it gets to that point, it is a hassle.
But I have to disagree with SD here - if you're a foreign language teacher and can speak the language which you are teaching, then if your ability in the country's local language isn't so hot, that's the only time when you can get away with it, I think. I am a foreign teacher - English in Japan. My English is awesome, but my Japanese isn't so hot. But then, what needs to be known is written down. The stuff which it's important to hear me pronounce isn't Japanese, it's English. That's the whole point of having a native speaker teach the foreign language in the first place!
On that note, though, how about this - I'm from New Zealand, so I have a New Zealand accent. Japanese people are by and large used to American accents in English, thanks to your tawdry globalisation through music and movies. So when they are used to hearing, for example, "gr(eh)ss" (that nasal, high-pitched "a"), and I say "gr(ah)ss" (the lower, more refined "a"), they can get a bit confused about what I mean, and some teachers have asked that I speak to the students in a faux American accent. Do you guys think it's more important for me to speak in an American accent to help with understanding, or in my natural accent to help with making them familiar with the wider range of accents out there?
Can't believe nobody beat me to that.