Continuity mistake: When the terrorists attack the van at the bridge, shortly after the explosion, you see the terrorists crossing the water in a boat. In the background you can see the van on the bridge with its doors open, shortly after this the terrorists are at the van doors demanding that the police open the van doors!
Continuity mistake: When the bookshop keeper runs from his store in Piccadilly he enters Aldwych tube station this is impossible as said tube station is a 20 minute bus ride away. Also when he gets on the train the conductor announces that the train will stop at Leicester Square, Piccadilly circus (were he just left from), and Oxford Circus This is impossible, as no train on the London underground makes stops at all those stations. He would have to change trains at Piccadilly circus.
Continuity mistake: When Jack rushes to save his wife and daughter from the terrorists on the freeway, there is a shot where he turns onto another road. Throughout this scene his seat belt goes from being buckled, to unbuckled quite a few times.
Continuity mistake: When Annette goes upstairs to the bedroom, we see a brief shot of her Uzi. There is no magazine inserted. Even the 10 round magazines stick out about half an inch and would be visible. When Jack picks up the Uzi after Annette is knocked out, suddenly, there's a magazine in it. (01:39:35 - 01:40:03)