Too Dumb to Live: What exactly made the Winchester any safer than Liz's apartment? While it's got big heavy doors and a rifle on the wall and Ed knows where all the exits are (and he can smoke), they actually probably would have been safer in the apartment, because the window was above ground level (Shaun himself could climb up to it, but he wasn't a zombie) and you couldn't even get into the building without being buzzed in. Even if the zombies somehow got in through that door, they could have barricaded the apartment door fairly easily. But they also wouldn't have had half so much booze.
Too Dumb to Live: He takes this to new levels and plays it for laughs. The characters need to get past a horde of zombies, and do so by acting like zombies to avoid drawing attention. When they are nearly to apparent safety, his phone goes off... and he answers it and starts cheerfully talking on the phone, less than ten feet from dozens of zombies. Previously, he had "accidentally" crashed their first car, giving him an excuse to drive a Jaguar instead. Following after the cellphone incident, the electricity comes back on and he starts playing a pub fruit machine, which draw the attention of a zombie in the same building as them.
Heel Face Door Slam: He almost redeems himself. But then he gets ripped apart by hungry zombies. In a deleted scene, he actually managed to apologize before being killed.
Jerkass: However, unlike Ed, he isn't at all likeable.
Jerkass Has a Point: Seemingly invoked deliberately. It's clear that he's correct in that Shaun's plan isn't very well thought-out, and his ultimate goal amounts to little more to sitting around and waiting for rescue. However, considering that he himself rarely has anything to offer but unhelpful snark, and that he just makes things worse on the rare occasions when he actually tries to do something, it's clear that he's Right for the Wrong Reasons, his criticisms of Shaun's plans being more out of personal dislike for Shaun than him actually having any idea of what to do, keeping him from being remotely sympathetic. Even when he's right and is actually ready to do something about it (when he was ready to shoot the now-dead Barbara before she could revive as a zombie), he can't do it without being a complete twat about it, and he ultimately wimps out and makes Shaun do it.
Know-Nothing Know-It-All: As Diane points out, if he really was as capable as he was trying to act whenever he was putting Shaun down, he would have taken charge of the group himself, rather than following along with whatever Shaun was doing.
Love Makes You Evil: Everything he does is motivated in some way by his not-so-secret love for Liz.
Non-Action Guy: The most he does is empty a bin and throw it through a window.
"It's a lot of overblown nonsense, a lot of drug nuts running wild."
Jerk with a Heart of Gold: Shaun hates him and he acts pretty coldly towards his stepson at first, but it's later revealed that he genuinely cared for Shaun even after everything they did and said to each other.
The Cameo: Jessica Stevenson previously worked with Edgar Wright, Simon Pegg and Nick Frost on Spaced.
Hero of Another Story: Has a group of survivors just like Shaun (with a counterpart for every single character in Shaun's group), but she seems to be the only one who got out alive. Presumably kicked a lot of zombie ass off-screen.
"No, it's not. It's fucking Sunday. And I've got to go to fucking work in four fucking hours 'cos every other fucker in my fucking department is fucking ill! Now can you see why I'm SO FUCKING ANGRY? "
Deadpan Snarker: Whenever he has to put up with Ed's stupidity. Which seems to be often.
Full-Frontal Assault: He seemingly turned into a zombie during a shower, causing dead Pete to stumble around butt nude.
Jerkass Has a Point: Ed doesn't pay his rent, makes a mess, plays loud music at night and isn't even attempting to get a job. It's hard to dispute his assessment for why Shaun keeps Ed around, even if the two are best friends. More infamously, he's the one who tells Shaun to sort his life out, which he spends the rest of the film trying to do.