Factual error: During the subway fight, Hellboy rips a payphone off the wall, which sparks as he does so. A phone does not have a voltage source that would be high enough to spark.
Revealing mistake: During the scene in which Rasputin is resurrected, at one point, Ilsa wipes some snow off a wall then checks her book to see if she can match a symbol. When she opens the book, some snow lands inside of it... and it is incredibly obvious that the snow is fake. It looks like pieces of torn up paper.
Other mistake: When the camera pulls up from Hellboy embracing the dead Professor Broom, you can see that several of the evidence numbers are present more than once. Evidence numbers exist to identify and correlate different pieces of evidence without doubt in photographs of the crime scene. It would just be nonsensical to re-use them on different pieces of evidence on one and the same crime scene.
Continuity mistake: When Hellboy chases Sammael into the subway, in one shot, he's slightly leaning to his right. In the next shot, he's leaning to his left with no time to change. This has nothing to do with the camera angle.
Visible crew/equipment: In the scene in the museum, when Abe shows John Hurt what happened in the building, a reflector screen is reflected in John Hurt's glasses.
Character mistake: Tom Manning criticises Hellboy for using a lighter, (correctly) telling him to use a wooden match instead. But he then lights a match and immediately puts it to the cigar, instead of waiting for the sulphur to burn off and using a pure wood-fuelled flame to light it. He's not as well informed as he thinks.
Revealing mistake: When Kroenen cuts open the statue to get the Sammael container, the slash on the statue is actually at a different angle than he actually slashed it. Probably the actor missing the correct angle, which is admittedly difficult.
Chosen answer: According to the comic books, his name is Anung Un Rama, or 'World Destroyer, The Great Beast.'