Other mistake: The brief chess game (four moves) shown in the beginning of the movie makes absolutely no sense. For instance: There are no white bishops on the board, but after the human player taps a few buttons, the computer says that he just moved one. Within the two moves described first, the positions of the pieces change completely. In addition, some pieces are now gone and there are new pieces on the board. It's like an entirely different game. The final move is said to have been made with a black rook, which is impossible. In the shot shown before this move, there is not a single position available to that chess piece that would result in an instant checkmate. Nothing in the editing indicates that these few short shots are supposed to be viewed as separate games. (00:04:50)
Other mistake: When Doc uses a computer to watch/simulate dog cells being assimilated by a "thing" cell, we can see a single cell fusing with multiple dog cells to imitate them. This process would lead to the dog being digested until it remains only one cell, and not to the replacement of all of its cells by the imitators. (00:40:30 - 00:41:25)
Suggested correction: The computer simulation isn't showing just one cell taking over an entire dog, but showing how the creature can get the genetic makeup of whatever it touches and replicate it perfectly.
I think it's fair to consider this a goof. John Carpenter states on the director's commentary his goal through this sequence was to demonstrate the life cycle of the Thing, and acknowledges that the visual isn't accurate for that purpose.
Pretty much the entire rest of the movie unfolds as though the simulation showcased the Thing spreading / multiplying: it's followed by text saying the entire human population could become "infected" after a certain amount of time; it's not until after this scene that anyone besides Blair is worried that one or more of them has been taken over. It's a valid movie mistake because the movie itself seems to assume the audience saw something different than what was actually shown.
Other mistake: When Doc's arms are being ripped off by Norris' chest, his left arm is cut by the teeth but his right arm is pulled off above the wound like rubber. (01:13:00)
Other mistake: When Blair goes crazy with an axe, they put him in the tool shed and Doc injects him with something to calm him down. The problem is: Doc injects him in the inner elbow, but wipes the upper arm as if that's where the injection went. Plus you only inject in the inner elbow when you want something IV, but there was no tourniquet, no searching for a vein. It should have been given IM, into a muscle, like the upper arm.
Other mistake: Blair somehow manages to fire seven shots with his six-shot pistol.
