Revealing mistake: When Stu is tempting the sniper to see if he will really shoot, the sniper shoots the phone booth, shattering the window, and supposedly hitting or grazing Stu's right ear. When Stu lifts his head, you can see his bloody ear. A few shots later, Stu's head is turned so you can clearly see his fresh wound. If you look closely, you can see Stu's real ear folded back beneath the fake latex one. This happens several more times in the next few minutes of the movie. (00:31:40)
Revealing mistake: At the end of the film when the Pizza Guy is wheeled towards the ambulance and is identified by Stu, you can see the corpse breathing. His neck and chest move slightly. (01:09:25)
Revealing mistake: Near the start, in the first few minutes, in several shots you can see barriers that are separating the crowd from the set. They are right back, so they couldn't be too visible.
Answer: The pizza man is intended by the Caller to be a decoy so he can get away. The Caller sends the pizza man to the phone booth so that Stu will identify him later in the apartment, giving the police a convenient answer to the mystery while the real Caller escapes. In fact, at the end of the movie, the Caller comes to visit Stu - obviously he's not the dead pizza delivery man.
Phoenix