Revealing mistake: When MacReady burns the one "Thing" with the split head, in one shot it walks by MacReady in the foreground, and you can tell in that shot that it is just a still dummy burning, as it isn't moving at all. It just sort of floats past with its arms at its sides, while in the previous and next shots it is wildly moving around, arms flailing.
Revealing mistake: The dead woman who is found at the beginning of the movie takes a rather deep breath at the end of the shot. (00:02:40)
Revealing mistake: Throughout the movie, practically every victim ends up with a broken, twisted neck. The "special effect" used for those deaths is...the actors wear their jackets backwards. It is made even more evident by the plot twist at the end.