Continuity mistake: In the 1982 movie, the alien ship is uncovered by the Norwegian scientists using thermite. (As seen on the films discovered by the Americans.) In the 2011 movie, it is uncovered when the Thing gets back into the ship and starts up the engines.
Continuity mistake: Near the end, when the dog-thing escapes from the camp look closely, its not the same dog, that's because the standin is a different dog altogether.
Continuity mistake: When Kate scoops up the fillings with a tissue after discovering the blood in the shower, the tissue and blood shrink and change between shots.
Continuity mistake: When Carter tells Kate to put her headset on in the helicopter, the microphone on her headset moves closer and further away from her face between shots.