Factual error: In the final fight scene with Malekith, Thor falls through a portal that brings him to Charing Cross station, where the lady on the train tells him he has to ride 3 stops to get to Greenwich. Charing Cross is not on the Jubilee Line and so not directly connected to Greenwich - even then it's a lot more than 3 stops.
Continuity mistake: The wounds on Thor's forehead change from fresh to dry then fresh back again, and even become larger in the last fight.
Continuity mistake: When Loki is nearly sucked into the vortex, his hands are empty. However, in the first shot after Thor rescues him when they fall to the ground, he suddenly has his dagger in his left hand.
Continuity mistake: Sif has a wound on the left side of her forehead which disappears when she arrives at Asgard.
Continuity mistake: After the battle of Vanaheim has ended, the scene cuts to Asgard where Odin watches people practicing battling and is joined by Thor. The shot after Odin says "Vanaheim secure?" shows Thor with his head half turned to Odin. Next shot he's suddenly looking at the battling people without his head turned an inch.