Continuity mistake: In the scene where the helicopter is outside the castle, the entry team dons their diving gear to enter the water. They put on gas masks with one viewing panel. When the shot changes to a water view the entry team is wearing scuba masks, which have their viewing panel divided in half by a black line. When the team emerges from the water within the castle in the next shot they are back to wearing masks with one window.
Revealing mistake: When Selene falls into the tunnels of Tanis's lair where the lycans are, you can see the pad she lands on. It's almost passed off as falling snow, but watch how as she lands the 'ground' squeezes like a pillow. This was pointed out in the director's commentary.
Continuity mistake: After the fight on the barge between Michael and Marcus, Selene tries to revive the impaled and seemingly dead Michael. At one point she rips his shirt open to pour her own blood into his wound, then the shot changes to her face, then changes again, slightly further out. It is in this shot, you can see Michael's shirt is still intact.