I think Andrew-Lee Pottsdoes a passable, though not perfect, American accent. I didn’t realize that he wasn’t an American when I saw Return to the House on Haunted Hill for the first time. It wasn’t until I’d seen Primeval, Ideal, and Alice, and then rewatched RttHoHH that I picked up on spots where he slipped up.
As for faking US accents, it really depends on what the accent in question is supposed to be. Midwestern accents can be faked fairly well, southern accents can be either good or terrible, and pretty much no one does a good Northeastern accent, especially the Maine accent (evidence? Storm of the Century. Not one of the actors, not even Julianne Nicholson who is actually from southern new england, hits the Maine accent spot on. This mini-series sounds as bad to New Englanders as the accents in True Blood do to Southerners) not even Americans who have been exposed to it. The largely Canadian cast of Haven is the least painful to listen to, though. My guess is that the midwestern accent is fairly well faked by Europeans/Australians/New Zelanders because it’s more common on US shows than either real Southern or Northeastern (mid-atlantic and north) accents.
I can’t watch The Closer because of this. Her attempt at a southern accent is just* that* terrible.