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: In the scene where Thor tells Jane to hold on, she's on Thor's right side and Mjölnir (the hammer) is in his left hand. As they are traveling through the Bifröst to Asgard, the position of each has changed. (00:28:20)
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.
Continuity mistake: In Asgard, right after Frigga has been captured, a Kursed Algrim is holding her by the shoulder. In the next shot he is holding her around the neck.
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.
Other mistake: When Kursed Algrim stabs Frigga, the sword goes in but doesn't come out.
Continuity mistake: At the end, Jane and the others are sitting at the table eating. Right when Jane says "we committed treason as we left" she is holding her spoon. The shot changes and now the spoon is in the bowl and she picks it up.
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: When Thor, Loki and Jane make their escape from Asgard, Jane is lying on her left side. The following cut, she is on her right side.
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: Lady Sif's shield is pierced by an arrow during the opening battle. In all subsequent shots, the hole vanishes and the shield is intact.
Continuity mistake: As Thor and Odin watch the people practicing battling, Odin says Thor has earned his gratitude. Thor says "Thank you" lowering his head. In the next shot, his head is suddenly raised. (00:10:35)
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)
Chosen answer: The Tesseract on Earth posed a great threat to everyone. Thor wanted to get it and Loki to Asgard as soon as possible. If he first had to track down Jane in Norway, that could take a while and leave the Tesseract vulnerable.
Friso94