When Dr. Doom is bending Reed Richards finger back when he's super cooled, Dr. Doom's hand slips and lets Reed's finger go at the end of the shot, but it continues to make the crunchy noises as if he is still bending the finger.
Reed and Sue's warning to Johnny about approaching 4000 degrees kelvin is wrong on two counts. Not only is this not approaching the temperature of the parts of the Sun that actually 'burn' hydrogen (the Core and the Corona, which are a thousand times hotter) but as a single point of heat only the air in the local vicinity would burn - not the whole planet's atmosphere. A far greater risk would be what in fact happened: objects near by would set alight and burn/melt.
Reed asks Doom a "Chemistry 101" question about what happens when a metal is rapidly cooled. Since there's no chemical reaction involved in cooling metal, he should have posed it as a "Physics 101" question.
As Von Doom is watching Mr. Fantastic on his monitors as he's doing the equations on the blackboards, the final underlined statement is already on the board - then Mr. Fantastic goes and writes it on the board, underlines it, and retracts his arm.
When Johnny Storm is coming out of the motorcycle show, he has his arms round the shoulders of two women. In the next shot he is linking arms with them then in the next shot, his arms are back round their shoulders.
When Sue goes invisible for the first time on the bridge, she has high heeled boots on, as she disrobes... her feet are bare but she didn't take off her shoes nor is there any sight of them when Johnny picks up her clothing from the road.
When they are discussing building a machine to reverse their powers, Ben has a piece of watermelon on his fork during the closeup on him as he starts to ask Reed if it is possible. As he continues the sentence, the watermelon has disappeared when the scene changes to a group focus.
When the waitress sets the stack of pancakes in front of Ben in the diner (with Von Doom), the butter pat slides off the side. In the next shot, the butter has magically jumped back to the top center of the stack, and stays there for the rest of the scene.
In the fight scene between Ben and Doom, they fall into a hotel pool, showing a guest on the floor below looking at the ceiling as water starts to leak. In the sequence they keep jumping from the man trying to get in his room to the ceiling. As the water is rushing down the hall, from Ben's prospective we see the hall empty, but then they switch back to the man just getting in the door in time as the water rushes by.
Victor Von Doom's facial injuries after the space station incident change from scene to scene. Starting at similar size on both the left and right, then only on his right (and longer) with no trace of the ones on his left. Although the increasing length of the right one could be due to his condition, this does not explain why the left one vanished.
(at around 57 minutes) When Von Doom goes to grab a towel in his bathroom he receives an electric shock to his right hand but looks to the left, all other shots in the rest of the scene show him looking left and it being on his left hand.
When Reed is testing Johnny Storm's ability to "flame on" in a test chamber constructed of titanium, the recorded temperature exceeds 4000K. Titanium melts at 1941K, and boils at 3560K. As there were slots in the chamber walls, it is unlikely that any insulation would have been effective in maintaining the integrity of the chamber.
New York City Fire Department Ladder 54 is an aerialscope style "Tower Ladder" featuring a platform at the end of the ladder, not a "straightstick" that lacks the platform. In fact the FDNY currently has no midmount straightstick in service.
In the bridge scene, Johnny and Reed encourage Sue to turn invisible so she can sneak past some police officers, forcing her to disrobe. After she sneaks past, Johnny and Reed run up to her carrying her clothes, they manage to pass by the police officers themselves since the officers are too stunned by seeing Sue turn invisible to notice.
The Thing's weight is inconsistent throughout the film. For example, at the beginning, he's heavy enough to collapse a hospital bed while simply laying in it, but when he's thrown into a moving car by Dr. Doom at the end of the film, he does little more than dent the hood and apparently has little impact on the vehicle's maneuverability.
Although they are supposed to be in the fictitious Baxter Building, the lobby and the elevators are clearly those of the real Empire State Building. Furthermore, the Empire State Building is even clearly pictured in a huge wood inlay in the lobby.
When Ben stands on the beam that the jumper has retreated to on the bridge it bends several inches under his weight. After he jumps down onto the bridge surface it springs back to normal.
Not only would a bend in such a beam be a permanent deformity, a mass large enough to cause such a bend would hit the asphalt with enough force to cause a similar depth crater - which does not happen. In fact if his weight remained at this level through out the movie every foot step he made would break paving slabs, floor tiles and pretty much every thing he walked on, and put him crashing through any floor not reinforced to bank vault levels in any multi-story building he tried to enter.
When Johnny jumps off the building to avoid the missile, he flames up. As he shouts 'woo hoo' the 4 on his costume is back to front and on the other side, meaning that this shot was mirrored. This was fixed on the DVD release.
The goof item below may give away important plot points.
Errors in geography
When Doom is fighting with Sue Storm, we can see the flash of Ben changing back into the Thing in the penthouse of the Baxter Building which is several blocks away. Less than a minute later, Thing crashes through the wall to save the day.