Revealing mistake: The Thing takes a swing at the captain after the captain opens the door. As the Thing swings his arm, he takes out a chunk of wood out of the door. If you step through the frames on the DVD, you can see the wood leaving the door a full second after the Thing has hit it. A small explosive charge that was not in sync with the actor. You can also see the outline of where the wood comes off before he swings his arm. And one more thing, his arm does not touch the door or even comes close to where the wood comes off - a safety precaution I presume.
Revealing mistake: The search team uses thermite charges to melt the ice around the saucer. After the initial explosion, the ground begins to rumble and the members of the search team all dive to the ground as the space ship itself goes up in a tremendous blast. Look at the sled dogs when the scene cuts from the explosion to the team huddling on the ground. They stand there calmly observing the scenery - no barks or yelps even though a violent explosion has supposedly rent the ground about 100 feet away from them.