When the taxi is slowly going down the motorway approaching the outskirts of Manchester, you can see the blue motorway signs on the left, the white painted line on the shoulders, the streetlights in the middle of the motorway, and the gray overhang across the motorway they are just about to pass under, all bouncing around as if it's some type of CGI overlay that is unsteady.
While escaping the military-guarded location, Jim is wearing a green shirt and his hands are bound. After scaling the wall and dropping to the other side, his shirt has been caught on the razor wire atop the wall, but his hands are still bound.
During dinner, when the infected set off a tripwire outside the perimeter, Maj. West is wearing his 'Blues', No.2 dress. Immediately after the action, when he is explaining to Jim about giving his men women, he's changed into his DPM smock (battledress).
When the camera pulls back to show Manchester aflame, a row of flashing lights is visible in the distance. It's the police keeping traffic back so that the road looks empty. About 2 seconds later, a car drives by in the distance.
The blockade is supposed to be situated North East of Manchester. Yet during the scene when Jim escapes back to it, the signs read Blackpool and Fleetwood, and also shows signs for Lancaster and the Lake District. These signs are only seen on the M6, running to the West of Manchester.
Frank drives his taxi through the Blackwall Tunnel because "it's the most direct route to the other side of the river." They start on the north side of the river and head north toward Manchester. Going through the Blackwall Tunnel would actually take them south.
When the main characters are leaving London, they stop off at the super market for food. When inside the store, it is clearly illuminated by artificial lighting. There is meant to be no power in the city. Strangely when they leave there is a shot of the outside, which clearly shows the shop in complete darkness.
When Major West and the unit he belonged to were deployed to the original motorway barricade, or whatever mission they were initially assigned, chances are, with the speed and haste that the infection spread among the population and masses, they were probably deployed immediately with their camouflaged field uniforms they were currently wearing and all the necessary equipment, NBC gear, weapons, ammunition, explosives, that they could carry. Yet we see him at the dinner in his dress uniform. It would be highly unlikely that he would have put that dress uniform in his equipment kit bag or backpack, which each individual soldier either hand carries a carries over his back.
With no electricity in London there would be no lights, yet when they going to the grocery store before they leave London, it is well lit and the light is not coming from outside the store. In reality, the store would be almost pitch black except for some light coming in through the front windows facing the street.
Rage can spread from human to animal or animal to human, by biting, or infected blood landing in the victims mouth, eyes, or nose. The movie has no infected dogs or birds of prey. The virus may require a host closely related to humans, like the chimps from which the outbreak originally began. This is reinforced when the film shows uninfected horses.
The common trope of the zombies being undead with a craving for brains (or human flesh) is notably and deliberately averted in this film, pinning the reason for the devastation on the rage virus which turns people into violently aggressive killers - but this opens up a considerable plot hole: Why don't the rage victims kill each other? "Normal" zombies don't because the undead kill the living but the rage-infected seem to act more like a dog in the final stage of rabies, attacking anything that moves and/or makes noise - the infected have no reason not to attack each other.
When Jim and the 3 others go into the Budgens grocery store to pick up supplies before they leave London, after 28 days, the smell of the inside of the grocery store would have been so repulsive, if not on the verge of a bio-hazard in itself, due to all the rotting, fermenting and decomposing milk, dairy, fish, poultry and meats, that as soon as they walked into the store would have, at the very least, make their faces wince at the stench and at the very most would have made them turn around and leave the store immediately due to the intolerable and unventilated pungent odor.
Since the zombies in this movie aren't undead, or - presumably - physiologically altered in any significant way (the writers have said that they liked the idea of a plague that altered people psychologically instead), their metabolism must be more or less that of a normal person. Hence, they would die of thirst in a few days, or, if they drink, starve to death in a few more - especially since it doesn't seem that they eat who they kill, or much of anything else (we see no half-eaten corpses or anything like that, groceries are left untouched etc.).
About eleven minutes in, someone walks up a distant sidewalk. Since Jim is calling out for someone, that person would've heard Jim, or Jim would've seen him. Clearly, the person is not part of the movie.
The goof items below may give away important plot points.
When the Jeep returns to the mansion after picking up Jim, Selena, and Hannah from the roadblock, two soldiers open the gate to let the Jeep onto the grounds. The black soldier is Private Mailer, the soldier tied up in the backyard. In the DVD commentary, Danny Boyle said he was so impressed with Marvin Campbell in the few small scenes he'd shot that he decided to cast Campbell as Mailer. All of Campbell's previous scenes were deleted, except the shot of him opening the gate.
After Jim stabs Pvt. Jones with a bayonet attached to a rifle, Jones is shown falling forward onto the rifle. This would've caused further damage and possibly kill Jones in the process. However, seconds later, when Major West walks up to Jones to comfort him, not only is Jones still alive, but laying on his back and the rifle nowhere to be seen.
When Frank has been shot and the soldiers are approaching his
body, you can see a cameraman lying down at the right of the screen in front of a concrete block. He's clearly visible for about three seconds.