Continuity mistake: When Windows breaks the glass to the gun cabinet, he takes out one of the shotguns and picks up some ammo. At the left hand side of the cabinet, there is some remaining glass in the cabinet along the side. The glass along the left side vanishes when Windows places the shotgun on the floor. (00:59:15)
Continuity mistake: Back at the research station, the researchers are looking at some debris from the spacecraft that is placed on a cloth on a snooker table. There is a guy with a grey sweater with his hands in the debris and a guy in a brown jumper also holding the debris. In the next shot, neither of their hands are located on the debris or cloth. (00:40:50)
Continuity mistake: Just after MacReady overhears the dogs barking, he runs over to the fire alarm, breaks the glass with his beer can and pulls the fire alarm. After he breaks the glass, there is a piece of broken glass located next to the alarm. But in the next shot, as he removes his hand, the piece of glass has vanished. (00:30:10)
Visible crew/equipment: Bennings tells Nauls to turn down the Superstitious song and Nauls skates over to the radio, but then doesn't turn the radio down at all. The shot then cuts to a shot of the medicine room which then continues as a panning shot and pans into the next room. Just as the camera stops panning and the shot remains still, there are a few stage lights visible reflected in one of the cabinets on the right hand side of shot. Those certainly aren't lights because all of the lights in the room are switched off. (00:15:10)
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.
Character mistake: The spaceship is much deeper in the ice than frozen thing, indicating it was buried a hundred thousand years after the spaceship landed. Norris' calculation of the age of the spaceship wouldn't apply to the thing, which was hardly buried at all, by comparison.
Continuity mistake: When MacReady and the two other researches first discover the the spacecraft, there is a shot where the camera is in front of the three looking downwards into the hole. All three of them have their hands by their sides. In the next shot, the researcher on the left suddenly has his arms raised with binoculars suddenly in his hands. (00:38:20)
Continuity mistake: After the Norwiegans' helicopter has chased the dog-Thing to the American research station, the chopper flies around the station before landing on the ground. Before landing, MacReady is shown exiting the watch tower with a bottle of alcohol in hand. When he exits, the bottle is around his hip area. Then from an angle of MacReady low down, the bottle is suddenly raised slightly up to his chest area. (00:06:35)
Continuity mistake: Just after MacReady leaves Fuchs to do his work, there are several items on his desk, such as a lamp, conical flask and books. In the first shot shown after MacReady leaves, the lamp is about a foot away from the conical flask and the conical flask is a foot away from the books. Next shot, the lamp, conical flask and books are more closer to each other. (01:05:10)
Continuity mistake: In the opening scene, a Norwegian helicopter is flying across the Arctic. The co-pilot is half outside it. From the exterior angle, the co-pilot has a pair of binoculars and is looking directly downwards with the binoculars also positioned directly downwards. In the next shot, from a side angle, the binoculars are suddenly elevated and he is looking directly forward. (00:02:55)
Visible crew/equipment: When Windows is in the radio room, he is trying to communicate with McMurdo. Doctor Blair then enters the radio room and approaches him, tapping his shoulder. Windows then pulls his headphones down from his ears and has them placed around his neck and he then says to Doctor Blair, "Nobody." Just as he says this, there are two white screens visible in his glasses. (00:11:00)
Continuity mistake: When MacReady is recording the stuff he knows about the thing, a glass of alcohol is on top of the tape recorder, located near the front of it. The camera then changes to a close-up of the recorder and the glass is now near the back of it. (01:04:00)
Continuity mistake: When Doc is defibrillating Norris, in the shot before he defibrillates him and we see it is actually the thing, Norris' eyes are definitely closed. In the next shot, just as Doc bursts through Norris and the Thing's intestines are revealed, Norris' eyes are suddenly open. (01:15:20)
Continuity mistake: When MacReady and Doc are examining the abandoned shack, MacReady comes across a portable video unit and MacReady then wipes off the snow and dust off the unit. From the first shot of the unit, we can see part of the unit is wiped so far, we are able to notice the unit itself. The visible part of the unit is located in the middle of the unit at first, but after Doc states the papers are in Norwegian and the shot cuts back to MacReady, it is now the edge of the unit that has the top of the unit visible. (00:20:00)
Continuity mistake: MacReady leaves the room so Fuchs can continue to do his work. The shot changes to an angle from behind Fuchs where he is shown writing on his paper. There is a conical flask visible at the back of the desk with some blue liquid in it. In the next shot, the liquid in the conical flask is suddenly just clear liquid. (01:05:10)
Other mistake: Blair somehow manages to fire seven shots with his six-shot pistol.
Continuity mistake: When MacReady tests Naul's blood sample, in the close-up shot, the items on the cardboard box change by comparison to the wider shot before. The revolver moves and the bloody scalpel appears from nowhere. (01:25:21)
Visible crew/equipment: When the "Thing" monster bursts out of Norris' chest it rises up to the ceiling and grabs onto an oblong-shaped ventilation shaft. MacCready steps forward with his back to the camera (getting ready to burn it) and in this shot if you look at the adjacent pipe on the ceiling you can see the hand of a crew member. It looks like the crew member is there to steady or grab the monster puppet if it falls. (01:15:45)
Continuity mistake: When in the helicopter, the Norwegian men are both wearing different types of goggles, but when they're out of the helicopter, they both have the same type of goggles.
Visible crew/equipment: Just after Nauls is told by Bennings to turn down the music the film cuts to a tracking shot going towards the rec hall. At the very beginning of this tracking shot keep an eye on the lower half of the medical cabinet, and you can easily see the dolly that the camera is being pushed on. If you look just above the dolly you can make out the blue sweater sleeve of the crewmember pushing the camera as well. (00:14:55)