I’ve heard David Tenant’s was bad on the American version of Broadchurch.
Oddly enough, I also heard the Karen Gilan’s was terrible on that Selfie show. Her real accent is pretty thick.
I also remember that Shirley Manson tried to do an American accent on Terminator, but they gave up on it after an episode or so. Hers is probably the worst I’ve seen since her real accent is super thick and she isn’t a trained actress.
James Callis tried to do one on Eurkea, but it was horrible. His real accent is very distinct and hard to override.
Julianne Moore tried to do a Boston accent on 30 Rock, but it was so bad she might have been kidding. In fact, I’m pretty sure she was.