When Sam is talking to Dr. Ren about Henry's decision to commit suicide, Ren's beard changes length between each camera shot, inside and out of the hospital.
During the chess game, the move "king's rook to e3" was announced. In fact the rook was moved to e1. The next move, "knight to c3, check," didn't put the king in check and Sam didn't move the knight there.
When Dr Sam Foster is counting Lila's bottle of Klonopin, it says "100 mg", but Klonopin is dispensed in .5 mg pills.
All of the books in the "bookstore" that Dr. Foster visits as he is trying to find Henry have library identification labels on their spines, revealing that this was actually shot in a public library (the 58th Street branch of the New York Public library in Manhattan).
When Leon (Henry's father) was talking to Sam after his eyes opened, he said that "The first time I can see everything" and "I always thought you had brown eyes." If a man didn't see anything in his entire life (he is blind), he can not know about the color brown to think about it.
The answering machine in Henry's apartment has "Digital Answering Machine" printed on it, yet when the new message is played, it sounds like a cassette tape rewinding before the message is actually played. Digital answering machines do not have tapes to rewind so there should be no taped rewinding sound.
Many times throughout the film when an emergency siren is heard, the siren is not the shrill US siren, but an obvious European style siren.