Deliberate mistake: There are a number of things wrong with the roller coaster scene (besides the obvious impossibility of a crash like this actually occurring): 1) The restraints use ratchets to lock, not hydraulics. A coaster of this type wouldn't even have any hydraulic lines. 2) The attendants didn't check all the restraints. This is ALWAYS necessary, on ANY ride. 3) On any roller coaster, the Dispatch button (or "Start" in the movie) must be held down until the train is clear of the station. This is a safety feature to make sure the attendants are clear of the moving train. If the button is released before the train is clear of the station, it will stop. 4) At the bottom of the lift, the lift chain curves to follow the track into the station. This is impossible, a lift chain cannot curve horizontally, only vertically (normally at the top of the hill).
Deliberate mistake: When Hellboy is attacked by the spider-lady, as the spiders begin to descend on him to steal the sword, you can easily tell that some of the shots of the spiders coming down are repeated 2 or even 3 times, and simply flopped horizontally to appear different.
Deliberate mistake: When Selene and Michael are driving a truck, chased by Marcus, at one point in the chase Marcus flies directly ahead of the truck and stays upright in the air with wings outstretched, facing the truck. Given that the truck is travelling at high speed and Marcus is using wings for flying, it is just not possible. It can't be attributed to Marcus' inertia - he stays in front of the truck for a couple of seconds, long enough to lose any speed advantage he had before.
Deliberate mistake: In Saw III we learn that Amanda was the person who abducted Adam from his apartment. However, if you watch his abduction in the first Saw film, you'll see that the person attacking him has the hands of a middle aged man.
Deliberate mistake: Throughout the movie, Seagal's voice changes. In some scenes, his lines are spoken by someone else (with a much coarser voice) and dubbed in, which is confirmed by numerous sources over the internet.