Shaun not getting butchered between his house and the shop after the outbreak. His hungover state meant he more or less blended in.
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.
Because people are sleeping in the same bed with the undead and playing video games with them, there is more of a chance someone will be bitten and restart the Zombie Apocalypse.