Although Shaun's plan is played for laughs, he had the right idea - waiting it out was the best thing to do.
Whilst underplaying his injury in true Stiff Upper Lip fashion - "I ran it under a cold tap!" - Phillip references him and Barbara having had their vaccinations when they went on holiday to the Isle of Wight, a seaside island community off the southern coast of the UK; a wight is also an old English name for an undead creature, not dissimilar in nature and appearance to a zombie, as Game of Thrones fans may well recall.
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.
This actually deserves a bit more explanation. First? The military has ACTUALLY SEEN ZOMBIES MOVIES. Secondly, Britain is much smaller then America, meaning less ground to cover. Third, there's less groups of heavily armed antigovernmental people, meaning that they don't have to worry about a rebellion. Fourth, it takes place in London, which would be first to recover.
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.
This actually makes more sense once you consider the fact that since zombie!Pete can remember things while he was alive, other zombies should be able to as well. They just remember him being a prick and would rather straight up kill him than turn him.
Another one that's not AS obvious from zombie movies? Most of the people who turn are people who GOT AWAY...as zombies go straight to disembowelment pretty fast.
Of course Shaun knew how to work the breakers in the Winchester. Not only is he a regular there, and appears to be a friend of the proprietors, he works in a household appliances store. He probably knows all sorts of tricks of the trade in regards to getting breakers and such to work in order to install their wares.
Possibly lampshade by Shaun actively reassuring the others that he knows how these things work and proceeding to adjust his tie as if to assert his department manager role.
Actually, the news does give an explanation at the end. Shaun just changes the channel so we don't get to hear it.
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.
During the ending while Shaun and Liz are watching TV, a woman who is keeping her zombified husband mentions that there have been "one or two" incidents with her friends, how many people are being turned into zombies, because their suicidally stupid friends are keeping their zombified friends and family with little precautions? Even Shaun is in on it.
That zombie Ed hits on the way to Shaun's parents, there is a good chance that he wasn't a zombie when they hit him, seeing as the news mentioned that it was the "bodies of the recently deceased" rising, which implies you only have to die to rise, not be bitten.
Ed got Philip killed (or rather, killed more quickly). It's very heavily implied that Ed purposefully wrecked his and Shaun's original car so that they'd be forced to let him drive Philip's Jaguar, and given that Philip and Barbara's neighbourhood was quiet right up until Ed smashed the car, it's only logical to presume that the zombies were drawn by the noise. Also, as Philip was already injured/bitten, he wasn't able to fight back or notice the zombie shambling up behind him until it was too late.
Also because Philip turned in the Jag, they were forced to abandon it and walk through everyone's backyards, leading to Barbara being bitten, Shaun having to kill her, David being ripped apart and then Ed getting bitten and zombified. Jesus Christ, Ed. Unwitting Instigator of Doomindeed.
These zombies are a lot smarter than in many other franchises, for example, Phil turns down the radio and Ed can at least in some way still play a game. This leads to a disturbing thought: just how much of the original is still in there? We'd like to hope that these are just vestigial memories without consciousness but...
Another example is Barbara, note that when she rises, she isn't hostile at all, she's just blankly staring at Shaun, even when he has a gun pointed at her. Then when David yells for Shaun to shoot her, she snarls, but she doesn't snarl at the nearest person (Shaun) she turns her head and snarls at David.
During the fight at the bar, when zombie!Pete bites Ed, Shaun yells his name. Pete immediately turns his head, meaning that yes, these zombies remember who they are after turning.
Its a good thing that Ed was left too weak to call out for help when the Army arrived. Had they discovered he was bitten, they would have shot him straight away.
. His hungover state meant he more or less blended in.