As far as I'm concerned, despite their disparity in looks, Drew Barrymore is Renee Zellweger's equal in annoyance. They're not great, but their mediocrity is no big deal to me.
The person whose "acting" style I have found most annoying by far is that Madonna, who apparently does not understand that acting involves much more than posing and mugging your way through a music video ever will. I was sent to a press screening of The Next Best Thing, and I've seen my share of awful movies and terrible performances, but--I just wanted to throttle her and her horrible character. I think I was more traumatized than annoyed. Just . . . horrible.
A distant second is Ryan Reynolds in Waiting. I hated the movie, and I especially hated the thick layer of smarm in which Reynolds was coated every second he was onscreen.
On the tendency to mistake lack of sexiness for annoying acting: As far as I'm concerned, John Goodman is just as fucking good an actor as George Clooney. But because he's fat, he's too often been consigned to shit like King Ralph. That's one example. Another is Kathy Bates, who is also very good (she's the main reason to watch the underrated Primary Colors), but ditto on the preponderance of "wacky" parts she's stuck with because of age/body. Much of the commentary on About Schmidt and the hot tub scene confirmed some of my worst suspicions about our culture's thinking. Hence, I go out of my way to avoid equating lack of magazine-spread hotness with absence of talent. I think that it's a tremendous deficiency in judgment if you're seriously annoyed just because someone onscreen isn't going to be occupying your wet dreams. I mean, "Renee Zellweger annoys me because she's ugly . . . " I have to say I find comments like that much more annoying than I'd ever find the relatively harmless Renee Zellweger.