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.
Continuity mistake: After Hellboy defeats the semi-vampiric heads, the Professor is seen destroying a small statue on his scroll representing them. Despite being destroyed, this statue reappears later in the movie.
Factual error: When Liz and Abe's plane crashes, it sinks far too quickly to be realistic. Also, from the sheer amount of force the plane hit the water with, both should easily have died. Obviously done for dramatic effect, but still a mistake.
Continuity mistake: During the Kappa battle scene, when the Kappa is thrown to land and some water spills from his head, there is a closeup shot that shows the spilled water becoming dark and discolored and then disappearing. However, in the next shot the water has reappeared, and is back to its original pale color.
Continuity mistake: When the Spider-lady is playing her koto, the number of strings on the koto changes between some shots. In the closeup shots of her plucking the strings, you can see that there is only six or seven strings. However, in some of the wider shots, you can see that there are at least 8-10 strings on the koto. This is most noticeable after the strings start to "bleed."