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.
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: 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: When MacReady says they are going to find out who's who, he tells Doc, Garry and Clark to move away from the others and one of them steps forward in MacReady's direction. MacReady then raises his flamethrower around the top half of his abdominal region. The shot then changes where the camera is in front of MacReady and the top half of his abdominal region is shown, but the flamethrower is nowhere in sight. The camera cuts to an angle behind MacReady and the flamethrower is back. (01:02:10)
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: 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: 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)
Continuity mistake: When the remaining men find Macready holding a flare to a bundle of sticks of dynamite, the sticks go from being loosely and haphazardly bundled together to tightly tied together and then back again in a matter of seconds. (01:12:45)
Continuity mistake: When Childs takes an ax to the supply room door where MacReady has broken into, there is a shot of him hitting the door high up. Then there is the shot of MacReady almost frozen. When the shot cuts back to Childs, the ax marks in the door are not consistent with the shot from a few seconds before. (01:12:50)
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)
Continuity mistake: When Doc is trying to revive Norris and his arms fall into Norris' chest, he is wearing long sleeves down to the wrist. In the closeup of Doc's arms being ripped off, the sleeves are pushed up to the elbows and the forearms are bare. (01:15:15)
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)
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 the thing is on the lab table, and the severed head starts walking away, Mack torches it with a flamethrower. At one angle, you can clearly see that fire is not coming out of the hose. It is just a fire going off in the doorway. (01:17:20)
Character mistake: When MacReady is giving the blood test, the scalpel they are using is not properly sterilized after each person cuts themselves (shown when Nauls cuts himself, then when Windows goes next: all he does is wipe the scalpel on his pants). Using the same scalpel seems like an extremely stupid thing to do as Fuchs told MacReady that even a small particle of the Thing could take over a person. (01:19:55)
Factual error: When the infected Palmer starts his transformation into the Thing, he has a series of fits and the creature 'falls', or leaps upward onto the ceiling. Watch closely...you can see a piece of paneling also 'fall' upward, when it should have fallen down. (01:23:20)
Continuity mistake: When Palmer is revealed to be a thing, he shoots up to the ceiling. Windows is ready to use the flamethrower on him. He has the flamethrower pointed up to the ceiling, yet when Palmer falls to the floor, in that split second, Windows changes into a completely different position with the flamethrower. (01:23:35)
Continuity mistake: When Palmer, as the thing, picks up Windows by the head his wardrobe is different as soon as he picks him up. The sleeveless motorcycle jacket he is wearing is missing and he is just wearing the green short sleeve shirt and the white sweatshirt. Then in the next shot he has the sleeveless jacket on again. (01:23:40)
Visible crew/equipment: When the "Palmer Thing" attacks Windows it lifts him up in the air. As it does this you can easily tell the monster is played by a member of the stunt team by the dark green T-shirt it's wearing. Palmer's clothing is different before and after this shot. (01:23:46)
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)
