Deliberate mistake: When Will is bound and brought before "Chief" Jack, Will says, "The compass!" and there is a close-up of the compass, as it hangs to the right of the long striped cloth. However, in all other shots the compass hangs to the left of the red and white striped cloth. This is a flipped shot - note the large buckles. (00:24:00)
Deliberate mistake: When Lex tests the crystal fragment, it knocks out all the power on the airplane Lois is flying in, yet the flight attendant's amplified voice can still be heard over the speakers. (00:30:40)
Deliberate mistake: After Ashley gets covered in mud, for the next five minutes or so of the movie the amount of mud on her constantly changes between shots, especially on the back of her head.
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.