Shaun not getting butchered between his house and the shop after the outbreak. His hungover state meant he more or less blended in.
Likely helped by their speed. One of the DVD extras shows that, compared to Shaun, the zombies were moving so slowly that he would have to stop and wait for them a considerable amount of time every 50 meters to let them catch up and continue the chase. And the fact that they were so easily fooled by him ducking into a dumpster following the old "out of sight out of mind" cliche. He was so hungover that it took them too long to catch on that he wasn't one of them, he walked too fast for them to get too good a look at him before he was gone, and once he was around a corner, in the store, or in his house, the zombies that might've had the mind to follow would've had no way of knowing where he went.
The reason why Dianne was able to survive on the meat of David's leg according to the plot hole comic on the DVD. He was torn to pieces and there was no chance that the cause of zombification could've infected the leg.
The joke involving the winchester rifle in the titular bar is instantly more clever once you remember the rule of Chekhov's Gun "If a rifle is mentioned in the first act, then in the second or third act, it absolutely must go off!"
Why does zombie!Pete suddenly show up naked at the Winchester at the climax of the movie? Earlier, when Shaun first discovers that Pete's been zombified, he tries to pretend that everything's normal and casually invites him to join them at the pub when he's feeling better. Even as a zombie, Pete remembered the invitation, and he remembered that Shaun and Ed would be at the Winchester.
The military successfully dealing with the zombies (albeit late) and society bouncing back to normal after a while is part of the Cultural Translation in the movie. In Britain, the government is more outwardly powerful than in America, and more importantly, expected to be. And the idea of a crisis causing the collapse of society into an anarchic frontierland of impromptu formed, heavily armed bands is much less appealing due to the different geography and history of both countries.
Shaun's blind rage with Ed makes even more sense when you remember he's a smoker who hasn't had a cigarette since the previous day. Any smoker (or former smoker) will know just how irritable/borderline homicidal nicotine withdrawal can make you.
Pete mentions in his 4am rant that all of his colleagues are mysteriously ill. Given that this is the day before the apocalypse, it's likely they're all suffering from pre-zombie symptoms.
The zombies disembowel David rather than turn him into one of them. The guy's such a prick even the undead want nothing to do with him! That's a rare zombie example of Even Evil Has Standards.
The mere fact that we NEVER get a specific origin for this zombie virus. All we get is in-universe speculation.
We don't get to see what happened to the boy who was dragged back into the house by his zombified mother. Considering what most movie zombies (this movie included) do to humans that they overpower, some things are best left unseen.