Factual error: While Bridger is watching the film of the Mafia boss following Beckerman he signals for the film to be stopped so he can look at the close up shot of the man. He is watching a 16mm film shown through a bog standard projector - stop a film like that for more than two seconds without closing down the projector shutter (this doesn't happen - if it did the screen would darken instantly) and it will melt and catch fire. This doesn't happen.
Factual error: Near the end of the film Butch is complaining about the living conditions they have to endure - jungles, swamps, snakes, night work - and Sundance sarcastically retorts "Bitch, bitch, bitch!" In 1908 the term meant just what it literally means: "Female dog." It did not adopt its current meaning of "complain" until much later. At the time the film is set - outside the context of "female dog" - it was considered to be a serious obscenity, and it would not have been used to describe something as ordinary as someone moaning about his living conditions.
Factual error: Bill Kempt rigs the sapphire asteroid with rocket motors to divert it toward the Moon. The motors are old and cranky, and to ensure that they fire on time he must, at some risk, lash himself to the rock and manually start the ignition. Upon lighting the engines he has several seconds to cut himself free, but in the scene he's shown swinging weightlessly as he snips the cable. If the asteroid is accelerating, he ought not to be weightless, but rather should be hanging behind the rock on his tether.
Factual error: Virgil's birthdate is given as 1935, but the flashbacks to his childhood have many mid-60's vehicles on the streets.
Factual error: The Saint picks up a newspaper, and reads an article that is, according to the headline, about the murder of the Englishman he met the previous night. However, if you actually translate the Italian in the body of the article, it is talking about an industrial fire on a ship.