I guess I could give generic slash peeves, but those seem to boil down to what everyone else has: bad characterization, bad reasoning for why two characters would get together, bad grammar, bad use of canon, bad writing, period. Bad Spike, no biscuit. So, specifics, and I'm likely to think in mostly Xander/Spike peeves, because that's what I read the majority of. Spike/Angel fics don't seem to set off my buzzers as much, in terms of badfic gongs.
A couple of things that get to me in X/S slash are Xander being written as much less mature than he should be for the time-setting, and the two of them being much closer than they should be, from the beginning of the fic.
There's an attractive hurt/comfort angle to making Xander the completely innocent one whom Spike either seduces or shelters, but it makes me cringe, when I see Xander thinking and behaving in a way that he demonstrably doesn't, onscreen. He's 19-through 21, during the time in which he knows Spike with any degree of familiarity. He's not a virgin (probably with men, yes, but he's had plenty of The Sex, and probably reasonably kinky sex, given Anya's scattered comments), and while he's quite likely to be nervous about getting involved with a man, he's not quiet and shy. (Okay, so I'm talking Xander characterization on a Spike board, but I think it's valid, nonetheless.) He can give as good as he gets with Spike, and isn't likely to be completely dumfuzzled and adoring of everything his partner says.
And the "Oh, we're buddies" opening to a story. Huh? Since when? They barely tolerate each other, and there has never, until the Glory arc headed into its final downward spiral, been a time when Spike was actually accepted among the Scooby Gang, without insults and suspicion. Even at the end of S5, Xander was pawing the ground and strutting his manly stuff about Spike being around, until the end of "Spiral." And Spike lives to insult him. So, a fic that starts out with the two of them in some hazy, undefined post-chip era, being more-or-less friends, is going to have to work pretty hard to convince me of that. Show me why. At least give a little background, telling me how because of event X, Spike has gotten closer to the gang, and Xander feels differently about him now, than he's shown to onscreen. I don't require all *that* much, but I have to set my suspension of disbelief on stun, if an author tries to set a story in a specific canon period, but doesn't have the characters acting as they would have at *that* time.
I make exceptions for stories that start out with the pair as lovers, if there's an explanation for that somewhere down the line, or the storyline shows me that it's not germane to the plot. They are, it happened, now here's the real story. That's fine. Er, possibly biased on that, because I've written a number of them.
Regarding messed-up S/X:
(One poster had written that she wants to see stories where Xander has a healthy self-esteem/not a mess. agree, but do have some issues with perfectly-happy-Xander, if one's trying to be canononical)
Yes, abused!Xander, unless very well done, makes my teeth itch now. Utterly depressed and suicidal Xander is also getting old. However, I don't think a story that shows *either* Spike or Xander as having a *healthy* self-esteem, can be completely in character, if it's set in Season 4 or later.
Xander *doesn't* have a healthy self-esteem. He covers his insecurities with jokes, or with attempts to appear more mature (season 6, imho, where he does feel better about himself because of job/apartment/fiancee), but he's still messed up, in canon. He's just getting better at hiding it. Spike, before recent events gave him some of his confidence back, has been one of the most mentally-and-emotionally-screwed guys around. I don't think stories that show them helping each other to feel better about themselves are played-out -- but I prefer subtlety. Show me the onscreen characters, or show me them as they would be when reacting to some major *new* trauma. Don't show them being utterly hamstrung by the same mental issues they have on the show, where they *aren't* basket cases.