It's odd because I tend to be annoyed when I hear an American actor doing an English accent. For instance, Natalie Portman (even though she's technically from Israel, she grew up mostly in America), in V for Vendetta, distracted me with that accent for the first half of the movie until I got used to it. There are other examples, but I'm too tired to think of them now.
Regarding English actors playing Americans -- like I've said before, I think Kate Winslet, in "Eternal Sunshine of the Spotless Mind" did a GREAT American accent...and Bob Hoskins is always good with them, in anything. As I've also said, Kristin Scott Thomas did the worst American accent I've heard, in some movie with Harrison Ford, the name of which escapes me.
Oh, and the way in which Keira held her drink is part of what threw me off, as far as the alcoholism thing was concerned. At the height of MY alcohol issues, I was actually pretty sloppy with my booze, spilling it all the time, and guzzling it with bits dripping all over. Maybe that has more to do with the fact that I was a beer drinker, and in The Jacket, Keira appeared to be going for the harder stuff. I guess it all just depends on one's perspective.