Corrected entry: In the scenes in the auction house, the auctioneer is wearing glasses the whole time, but when Prince Nuada holds up the creature in his hand, you get a brief look at the auctioneers face before the creature attacks and he is no longer wearing glasses.
Correction: It's not impossible or unlikely that he'd take them off. For instance, perhaps the auctioneer is farsighted. He wears reading glasses so he can read the auction manifest. When the strange intruder bursts in and brandishes an even stranger object the auctioneer removes his glasses, off camera, to get a better look at it.
Corrected entry: At the end of the movie, after the crown is whole and in Hellboy's possession, Liz decides to melt the crown down so no one could ever use it again to raise the Golden Army. But throughout most of the movie, Liz and her team had possession of one of the pieces of the crown. Why didn't she just melt that one piece when they had it? The crown never could've been put back together without it, and they would have never had to worry about the Golden Army.
Correction: Abe kept the 3rd crown piece a secret from the rest of the team, they did not know it was in their possession until Abe trades it for the Princess.
Corrected entry: In the subway scene, when Prince Nuada is training his right hand is closest to the blade, but then all of a sudden his left hand is nearest to the blade.
Correction: It's a simple, very quick switch to make. I just watched the scene and Nuada even appears to be winding up for the maneuver just before the angle changes.
Corrected entry: When the auction show is attacked the power goes out and the emergency lights come on, yet the television screens stay on?
Correction: Most likely running on emergency backup power. I can have my laptop running off of a power-cord, remove it, and the battery will kick on. They likely had an emergency power-source for the equipment, as they are dealing with very expensive items at the auction, and would want to maintain power constantly. Hence, the screens starying on.
Corrected entry: When the prince's nose bleeds, we see that the Princess's nose bleeds as well to show their link. Then a second later, both of their faces are blood free.
Correction: We see the prince wiping the blood away. It's entirely likely that the princess did the same (twins have a knack for doing things at the same time).