Plot hole: After an assault on the scale that's been witnessed, covering a wide area of London by extremely well prepared attackers, there's no way Marine 1 would fly to the airport at low altitude within easy range of missiles, and then when attacked, double back over the areas that have already been attacked where hostiles would still be present. (00:35:00)
Character mistake: When Mike and the SAS team leader first meet, the team leader introduces himself as Will Davis, Captain. However at the near end when they say goodbye to each other, Mike addresses him as Lieutenant. (01:07:35 - 01:25:35)
Character mistake: The news reporter at the start of the film states an autopsy will take place in the next 48 hours. British reporters use the terminology "Post Mortem" not autopsy. (00:09:50)
Factual error: The role of MI6 shown in the film actually falls under the purview of MI5, Britain's domestic intelligence service; as the country's version of the CIA, MI6's mandate is the covert collection of foreign intelligence overseas.
Factual error: When they spot the guy with the missile from the helicopter, the pilot says "we're being pinged", and Banning says "stingers." Stinger missiles are infra-red seeking, passively tracking the heat of a target, so there's no way to know if you're being tracked by one or not. As a highly-trained secret service agent, he'd know that. (00:36:50)
Other mistake: Colin Salmon in Box Command introduces himself to Banning as Chief Inspector. However, the rank on his shirt is of a Commander rank.
Factual error: London is shown to use the two-tone air raid siren to warn Londoners of the danger. The problem is, these sirens were decommissioned in 1992 following the end of the Cold War. (00:51:50)
Continuity mistake: When the helicopter has crashed and the President and Banning are standing outside, Banning removes his radio and earpiece and throws them to the ground. The earpiece is back in the next shot. (00:40:00)
Factual error: Throughout the Helicopter scene they are referred to as Marine One, Marine Two and Marine Three. There is a couple of problems with this. Marine One is correct as it has the President on board. Marine Two only has this call sign when the Vice President is on board, which he is not. And finally, there is no Marine Three call sign. (00:36:10)
Factual error: When the president arrives at the church, he gets out of the limousine, and they close the door. The Secret Service keeps it open for emergencies. The church door also gets closed, same issue. An agent would be there keeping it open. Then the entire motorcade is missing including the second limousine which is always present.
Continuity mistake: Secretary of Defence has her name spelt as "MacMillan" instead of "McMillan" (00:35:00)
Other mistake: The agent infiltrates Barkawi's daughter's wedding and sends a message to the US military to bomb the place remotely. On the agent's phone he types "Barkawi on sight" and clicks send, but there is no phone number or contact. (00:04:30)
Plot hole: Banning knows where there is an MI6 safe house but has "no option" but to head for the US Embassy. He could have gone for the Tower of London, Buckingham Palace, Knightsbridge Barracks, Downing Street, the Palace of Westminster or Scotland yard, all knee deep in security.
Suggested correction: The whole premise of not being able to go to the embassy is because they (the terrorists) will expect it. Banning also makes it clear to Asher that the entire security services are no longer to be trusted due to an insider. Going to any place "knee deep in security" is literally walking into a potential terrorist. The head of the UK response team even states they don't know who can be trusted and they need to eliminate the ones that have infiltrated the police forces. Hence the MI6 safe house.
Suggested correction: Considering the fact that there was a mole inside Scotland Yard, going there wasn't really an option.
Factual error: Marine One should have rushed directly to a warship on the water. The navy would have had many of them on alert well before, and Marine One would have had a pre-planned escape route secured by fighter jets.
Factual error: In such an insecure situation, the SS would have arranged a secure bunker ahead of time for VIPs on site. There is no mention of it.
Factual error: During the attack on the President at the church, where is the rest of the motorcade? The second limousine, several SS armored SUVs and the entire Counter Assault Team are missing.
Factual error: During the fight scene in the London underground, it's suppose to take place at Charing Cross station. Charing Cross is on the Northern Line and the Bakerloo Line. If you look at the map in the background that list the stations, none of them make sense. Green Park, Bond St and Baker Street are not on either of those lines, they are on the Jubilee. They skipped quite a few stations as well on the Jubilee. They picked random stations and made a map. (00:00:48)
Revealing mistake: When Mike is throwing Bakari around and starts his speech, pay close attention to Bakari's shirt. The padding is visible underneath it in some shots. (01:17:30)
Revealing mistake: When Bakari is fighting Banning with the machete, the blade gets stuck in some metal bars. In this shot you can see a break line visible in the blade where it snaps a few seconds later. (01:17:00)
Continuity mistake: Throughout the 4x4 chase scene the bullet holes in the windscreen keep changing place. (00:29:10)