Continuity mistake: At the end of the scene where everyone is trying to pull Mjolnir out of the crater, a SHIELD agent is seen pulling up in an SUV at the top of a hill about 50 yards away. Then when the shot changes to the view from where the SHIELD agent gets out of his SUV and is standing at the top the hill he is a 1/2 mile away or more.
Continuity mistake: The first time Jane, Darcy and Erik meet Thor, Jane says "Do me a favour and don't be dead. Please. Where did he come from?" But the second time we see them meet him, Darcy suddenly says "Woah, does he need CPR? Because I totally know CPR" right after Jane says "Do me a favour and don't be dead". Extended scene or not, Darcy's line was not there before and it makes no sense for it to be there now because Jane's line is still incomplete when she says it. On top of this, the word "Please" that Jane said earlier is completely gone.
Continuity mistake: At the end when Loki goes to lock the Bifrost on Jotunheim, he's wearing his helmet and carrying Odin's staff. He slides Heimdall's sword into the machinery to open the Bifrost and his helmet is gone. He freezes the electrical streams then when Thor comes in to stop him, Loki is wearing his helmet again.
Continuity mistake: In the desert scene where Jane, Darcy and Eric are getting out of the van to check on the person they just hit, they rush to Thor who is lying on the ground and inside the "bifrost footprint" circle. There are 3 shots following the first wide shot, which focus on Jane, Darcy and Eric, and then back to the wide shot of the 3 surrounding Thor again, but the bifrost print is gone this time. After the Asgard backstory we return to the desert scene and the bifrost print is once again present on the ground.