In the scene where Canaris' helicopter lands on the road you can see from the tail number ZS-HTN that the machine is South African. While who knows what manufacturer the British would be using in 2035 and given the civil breakdown, it would be unlikely to have a South African registration number.
Despite dealing with a "killer virus" that's managed to get an entire country quarantined, the soldiers at the blockade are wearing nothing to protect themselves from infection - just gas masks, which will help against toxic gases but do next to nothing against something as small as a virus - and even have exposed skin, such as their hands and necks. Full biohazard suits might be a bit much to expect but surely the joins in their fatigues should be sealed with tape and all skin would be covered, at least.
At the point where Eden and the rest drive away with the car through the emergency door, you can see clearly that the car scrapes against both sides of the emergency door as it is closing. However in the next shot, the car has no damage whatsoever.
When they are searching inside the hospital at the beginning and they are attacked by the punks, 2 of the ones that run through the door are killed several times. The same shot/scene is repeated several times with minor changes.
When the infected guy places the severed hand against the hand scanner, the fingers are curled. When he pulls the hand away the scanner shows a digital image as if the hand were pressed flat against it.
When Sinclair arrives at the wall the Sergeant that greets her says after asking why they call it "No Man's Land" that "there hasn't been a living soul south of that wall." Scotland is actually north of England not south.
When Sinclair escapes the punks, she and Kane's daughter run to meet her team at Glasgow Queen Street Station, but the station her team is eventually chased into, (or at least the set made to look like the station) is in fact Glasgow Central Station which is approximately half a mile to a mile away.
During the PM's brief, during which the contingency plan to isolate "All of London north of the river" is outlined, a map of London and the flood barrier is shown. Judging by the scale (approximately determinable by the readily recognizable kink in the Thames), the barrier only goes as far north as Hackney, and thus is isolating maybe 20-30 square miles out of the 600 or so square miles of London.
When the team first gets attacked in the APCs a man is able to shatter the windscreen with nothing more than an axe. This would be impossible because a typical APC has bullet resistant glass 3 inches thick.
If food is so rare that survivors are eating human flesh, why did the infiltration team encounter cows wandering on the road? Much of Scotland is very rural highlands that would be difficult terrain for anyone on foot. During the initial breakdown in order, it is highly unlikely that the survivors would scour the whole of the country for every last single cow before resorting to cannibalism. Only a few cows would need to survive to account for the herd that is then encountered, 30 years later and numerous (cow) generations later. (However, it *is* somewhat unlikely that none of the characters felt the existence of a large herd of apparently healthy cows to be worth commenting on.)
While a well-maintained lift would not fall even with the cables cut, due to the use of the Otis elevator brake after 20 years of disuse and poor maintenance, it is quite possible the brake is inoperative.
In the top secret satellite photos we see only few lonely people but when the crew arrives at the city they encounter hordes and hordes of "punks". However, the satellite photos are said to be from 3 years previous, the gangs may not have been as prominent as they are at the time period in the film.
Apparently the Bentley was stored for over 30 years. It is extremely unlikely it would run after this much time. Petrol is good for about six months (volatile compounds destabilize), the battery would be dead, and the tires would likely become harder/brittle.
After Sinclair and co are captured, Sinclair had the remnants of a can of beer poured over her head. The can would appear to be pristine and new. Given that it's thirty years since any cans were manufactured, how is this even remotely possible? Aside from this, there are numerous other examples throughout the film of materials that cannot possibly have been manufactured to a high quality since the virus swept the country and are in a condition that does not fit with either being low quality and non-machined or with having suffered three decades of wear and tear. (The paper plates handed out during the "Medium Rare" scene are another prime example.)
The steam engine, the boxcar and the carriages in background are South African. As British steam trains ran on Anthracite Coal, they have small fireboxes, unlike this South African one. Other than the Orient Express, no British train has carriages have steps as British stations all have platforms. The carriages are also still in South African livery. Similarly, boxcars have a narrow axle base, unlike these long, South African boxcars.