Other mistake: In the scene where John is in the apartment with the cat and Angela closes the door, John then says her name to get her to reopen the door. He says the wrong name, "Rachel" (the actress' name) instead of "Angela" (the character's name).
Plot hole: Constantine threatens demon Balthazar with the last Rites, so Balthazar goes to heaven where he for sure doesn't want to end. However, if it is so easy and possible even for a demon to go to heaven, why is occult expert Constantine still searching so desperately for the big way out of hell? He only needs to find a catholic priest who gives Constantine the last Rites.