When they stop at the display area with the Spear of Longinus, look behind the spear; there's a golden box with two angels on top of it, fitting the classic image of the ark of the covenant. See more...
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Continuity: Hellboy tosses Dr. Manning through the quickly-closing door to escape the pendulum on the bridge - he barely makes it under. Hellboy then spends thirty seconds dodging the pendulum, but when he dives for the door it's still closing at the same point and speed - just enough for him to pass.
Other: In the scene where we see Professor Bruttenholm talking to Myers about Abe's origins, we see the professor pick up what he specifically describes as "rotten eggs" from an open bowl and place them into a tube. The eggs have been sitting out in the open the whole time, but Myers only reacts to the smell once Broom picks them up.
Revealing: In the scene in the alley behind the museum where Hellboy first encounters Rasputin, Sammael has its tongue wrapped around Hellboy's arm. When Myers enters and shoots at Sammael, look closely at Myers' hands. Not only does the gun fire without him pulling the trigger, but the gun does not even recoil.
Continuity: At the end of the movie, when Rasputin is about to take away Liz's soul, the shot is over Rasputin's shoulder with Hellboy's front in view. We can see Rasputin's hand move from above Liz's chest to her jaw as he bends over. Then the shot changes to Rasputin's front. In this shot, the hand is back above Liz's chest and is moving to her jaw again.
Continuity: In the scene where Hellboy and his group arrive at Graveyard 16, a shot from farther away shows the graveyard in the background and in the foreground are the 3 vehicles in which they drove up. The two smaller vehicle's roof, hood and windshield are already covered in what looks like about 1 cm of snow, although they just arrived. Such light and dry snow that appears to be falling in the scene would have been blown off the car while driving, and a layer that thick takes a lot longer to develop.