Hands down, the worst fake British accent from a film star was Gwyneth Paltrow in Sliding Doors. She just makes me cringe. Ewan MacGregor's American is pretty bad too. But on the whole, I don't think Americans are as critical of accents as the British are, which is why everyone thinks Hugh Laurie's is so good. It's certainly not bad, and has gotten a lot better, but I found it a bit forced in the early seasons of House.
However, there's a big difference between professional actors with dialect coaches doing an accent, and regular people "doing" one. Americans faking British accents tend to sound either like a pantomime cockney or the Queen in the fifties. And my colleagues' idea of what "American" sounds like is just painful. They sound like pantomime New Yorkers. Even my colleague who is good at accents and can do West Country, cockney, RP, Scottish, Irish, Geordie, you name it, can't produce a decent American. Too drawly and nasally. But I'm with Legs Akimbo, many American accents, particularly the ones with really hard Rs, hurt my ears these days.
I've heard that David Tennant once did a pilot for a US show and his "American" was so bad they cancelled!
I had wondered if that was the reason his pilot wasn't picked up! Where did you hear this?