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.