Continuity: As Ethan and Sarah are on the beach after Ethan gets her out of the Hospital, Sarah is dressed in hospital gown and slippers, she slips off her slippers and than walks down the beach. In the long shot she is wearing her slippers and than the next shot is a close up of both of them and in the lower left corner you see her slippers sitting on the beach where she took them off.
Factual errors: A character incorrectly refers to the US Bank building in downtown LA as the "Liberty" Tower, when in fact the Tower is actually known as the Library Tower. The LA Public Library is across the street and gave up the air rights for the Tower to be built (which helped to rebuild the Library after two devastating fires). This was possibly a deliberate error, as the building is occasionally incorrectly referred to as the Liberty Tower (most notably by President George W. Bush identifying it as a possible terrorist target). However, a local resident of Los Angeles would most likely not make this mistake.
Revealing mistakes: About 1 hour and 5 minutes into the movie, during the city battle scene, there is a shot of S.W.A.T. team members firing on some flying dragons, who react with fireballs shot back at the officers. During this scene, you can see some of the officers running from the attack, in which a couple actually fly into the air well before the explosion appears on the rooftop.