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. (01:33:45)
Continuity mistake: When the aether enters Jane, just before she ends up back on earth, she is cross-like in a sea of red, but she is wearing a breastplate. She does not get given this until she is taken to Asgard 15 minutes later.
Continuity mistake: Sif has a wound on the left side of her forehead which disappears when she arrives at Asgard.
Other mistake: When Kursed Algrim stabs Frigga, the sword goes in but doesn't come out.
Continuity mistake: Thor has a massive boulder thrown at him. He ends up with a cut on his right forehead that moves to his left in another scene and back to his right in the next. Along with inconsistencies to the scar and placement at the end when he's holding Loki. (01:18:50 - 01:20:20)
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. (00:10:15)