My Ts parents were from a different country, so he didn't speak our language at home. He doesn't have an accent, but sometimes he messes up grammar (like once in three sessions). He'll say things that you could translate as "it make he afraid". Sometimes he notices and starts to stutter between the correct and wrong version, in those cases I tell him what's correct. Otherwise I don't mind.
Oh, and judging from his website, he also doesn't know how to capitalize certain special characters. That I find more annoying, I feel he should have learned how to use a keyboard in the last 30 years.