Continuity mistake: After pardoning his cousin with the melt stick, when he says "I'm stepping in it" Topaz can be seen with the melting stick on her left, in the next shot she has it in her right and then back to her left hand when she says "burnt toast." (00:39:00)
Continuity mistake: According to the previous film, Thor: The Dark World, Asgardian kings live approximately 5,000 years. (If I want to be cautious here, this statement is only valid about Odin and of unknown validity about other Asgardians.) But in this film, Thor says Odin fought Surtur 500,000 years before.