Continuity mistake: When Oskar intercepts Lacke's plan to kill Eli in the bathtub, Eli kills Lacke and drinks some of his blood, leaving some blood on her lips. She then kisses Oskar, which in turn leaves some blood on his lips. In the cut right after that the blood is gone from his lips. Later on it appears again, when he tastes it with his tongue.
Plot hole: After Eli's guardian is hospitalised for acid-burning his face, Eli hears on the radio that they can't ID him because of his facial wounds. When we see him in the hospital however, only half his face is injured, the other half is fine which would make a mirror composite easy for lab techs.
Continuity mistake: When Eli runs out of the basement and then runs outside, after she scares Oskar by licking his blood off the floor, there is snow everywhere. She then climbs up a tree, and when she is at the top of the tree there is no snow anywhere to be seen in the background. From the following day on the snow is back.
Continuity mistake: One of the bullying scenes has Oskar getting hit across the face with a branch, which leaves a long red cut. Shortly after that he goes to visit his father, and during this time both the bandage as well as the scar itself are gone. Later on in the movie they both reappear.