Continuity mistake: In the end, when the President is visited by the X-Men, he receives a blue binder, which is laid in front of him on the table. When they have left, you see a shot including the President's desk, and you can see that the only thing he has on the table are some sheets of paper, stapled in the upper left corner, opened up. Then the shot changes to a close-up of the President, and then back again, and you see the blue binder in front of him, closed, and the papers have disappeared. (02:01:40)
Visible crew/equipment: During the scene where Neo is talking to Agent Smith in the park area where Neo was talking to the Oracle, there is a close-up on Agent Smith's face. In his sunglasses you can see a bright white screen to reflect the light onto the faces of the actors. This isn't visible in any non-reflected angles. You can also see the cameraman on the other side. (00:51:15)
Factual error: The geodes occurring in the mantle during the film are impossible in two ways. Firstly, there are no gaps at those depths. The pressure is approximately 3.5 million times surface pressure, and it is not feasible that such structures could form, let alone be maintained. Secondly, the crystals inside the geodes are described as amethysts. Amethysts are a purple variety of quartz, and as any undergrad geology student could tell you, there is no quartz in the mantle, it simply is not stable at such high temperatures.
Continuity mistake: When Quatermain arrives in London, he is greeted by Reed who leads him down some stairs. In the shot where they're going down some spiral stairs, for some reason you see a different actor (who is clean shaven) posing as Reed, going down the stairs holding the umbrella in his right hand. Then in the next shot you see the "original" actor who has a slight goatee and is holding the umbrella in his left hand. (00:13:25)
Continuity mistake: Near the beginning, when Banner arrives at the lab with his helmet on, he removes the helmet when he sees Betty. A close-up of his face is shown and his hair is messy with part of his fringe on his forehead. Betty is shown quickly, then the same shot of Banner is shown again, but this time his hair is perfect.
Continuity mistake: Nino gets trussed up in silver duct tape. The boy gets bundled over the shoulders of one of the bad guys, and you can see that there is only a small amount of tape around his legs. They go straight inside the meat packing factory and suddenly in the next shot, there is a huge amount of tape around the boy's legs.
Visible crew/equipment: When My-ek and Du-ug are bowing to the cow before attempting to behead it, you can see a crewmember's hand in the bottom left corner of the screen, holding some sort of strap around the cow's legs (probably to keep it standing still).
Other mistake: Marvin survives the explosion by hiding in the refrigerator, though despite the massive blast, there is no singeing, burn marks, or even smoke around the holes that were torn into the front of the door before the explosion.
Other mistake: Garcia, in a manic moment, dips his right fingers into the bug's acidic saliva, then stripes his left cheek, where the acid eats into the flesh. A couple of minutes later, he dips the same two fingers back into the substance, and proceeds to stripe his right cheek, where the acid immediately starts eating through his skin. Oddly enough, the fingers aren't affected at all, despite being dipped into the goo twice.