Continuity mistake: In front of the favourite taxi diner, just after De Niro tells Wizard that he has some "bad ideas" in his head, you can see on his face and the wall behind him the characteristic intermittent pulse of emergency vehicle lights. The shot change, with Wizard talking across the cut implying continuity, and a few seconds later, right in that streeet, a police car with emergency lights on pulls over to apprehend someone. (00:47:25)
Continuity mistake: At Belmore's, Travis looks at the crimpled 20 dollars note in his hand; in close-up the top left (relatively speaking) corner of the note is folded perfectly towards him, while in the other shot there was no straight folding line. (00:45:35)
Continuity mistake: Travis walks out of Belmore to talk to Wizard. Right at the door he passes by some hoodlums; he is staring down in close-up a black kid with a chain. Another kid with a white T-shirt, carrying nunchakus, is behind him in that close-up, but walked already way ahead of him in the very first shot. (00:46:00)
Continuity mistake: Betsy walks away from the porn theater, and Travis follows her. He says, trying to yank her back by her arm "Wait a second, I wanna talk to you." Two prostitutes walk behind them. In the shot that follows, behind De Niro, the same prostitutes pop again in frame walking in the same direction, not having advanced at all and in fact being behind their previous position. (00:36:30)
Continuity mistake: Travis is in the Charles Palantine campaign office to talk to Betsy for the first time. When he asks, leaning on the desk "What do you say?", one of the volunteers, a girl wearing jeans and a T-shirt in horizontal stripes, walks behind him. In the next shot, with Cybill Shepherd playing with her pencil as she ponders an answer, the same girl walks again behind Robert De Niro, coming from the same direction as earlier. (00:22:25)
Continuity mistake: Travis' hair is medium length for most of the movie. But in some scenes (his chat with the Secret Service agent and Iris following) De Niro's hair looks shorter. Probably these scenes were filmed after the mohawk scenes, without enough time for his hair to regrow fully.
Continuity mistake: When Travis gets hit point-blank in the arm, there's a close-up of the gun falling down the stairs, which is re-established at the end when the camera pans back through the corridor showing the mayhem. But if you look at the shot that immediately follows that close-up, you can see Robert De Niro dropping the gun, that just bounces next to him, by the wall. (01:40:40)
Continuity mistake: The John stumbles inside the room in his dying moments and falls back with his arms spread out. In the shot from an elevated angle, with Iris screaming, you can see he is a certain distance from the radiator (and Iris' feet). In the POV shot from the door he is much closer, and when Travis is tackled by the mutilated timekeeper the dead man, Peter Savage has both arms up. (01:40:50)
Continuity mistake: When Iris sobbing says that Sport never killed anyone, her carb-bomb made of bread, jam and pure sugar is looking quite messy, with the slices of toast not quite matching in rotation and raised. When she picks them back up from the plate though, they are all perfectly matching and pressed tightly together. (01:26:00)
Continuity mistake: During breakfast, Iris suggests Travis that he could come to the commune in Vermont with her. De Niro is making a joker-esque big grinning smile in the two following close-ups, but there's another shot in between, with Robert De Niro visible only from the side in foreground, and he is not smiling at all in that. (01:28:10)
Continuity mistake: During the breakfast scene, Iris has her hair suddenly underneath the shades' arms, just for a single shot. It's the one when he asks her "You call that being hip?" and when asks who's a killer. (01:25:35)
Continuity mistake: In the hotel room, Iris is taking her shoes off. The heart pillow next to her on the couch changes position depending on the camera angle. (01:20:10)
Continuity mistake: Travis walks in the building where he is greeted by the 'timekeeper' of the prostitute. He asks for money for the room. Notice he has just a toothpick in hand, but when the shot changes and he checks his watch, he is holding a gun. (01:19:00)
Continuity mistake: Travis witnesses one guy beating another and dragging him away while he is in his car waiting for the arrival of the young prostitute. The corner is well lit by direct natural sunlight, and you can see the pavement, the working girls and the overweight woman walking along the building, all moving in the sun. Cut to De Niro approaching the girls, same street, roughly same spot including the graffiti landmark, and that sidewalk is in the shadow of the buildings. (01:15:10)
Continuity mistake: Listening to the music program after the robbery, Travis has the gun pointed up diagonally, leaning against the top of his head. Reverse shot and he has it pointed straight up, and only after a while it leans against his head. (01:10:45)
Continuity mistake: The robber is holding at gunpoint the store owner, arm outstretched. He turns around when Travis calls him, the arm still outstretched, straight, but when we see Travis blowing a hole in his face, that arm is bent, elbow close to the body. (01:08:50)
Continuity mistake: In the hotel room, Easy Andy puts on the bed the two suitcases and opens them. Look at the very distinctive gun with the mother-of-pearl grip. It points left in opening shot and close-up, but when Andy picks the 44 Magnum up, the Model 36 is now pointed the opposite way. (00:54:45)
Continuity mistake: During the lengthier part of Wizard's un-Russellian rambling, De Niro is holding the cardboard box upside down compared to the rest of the scene (easy to spot because of the blue label). (00:47:30)
Continuity mistake: While Wizard is commenting on the bit about 'f**s' in California, Travis who was still getting his order from the Belmore clerk is suddenly already midway towards them across the room. (00:45:10)
Continuity mistake: Betsy opens the door of the taxi and tells Travis that she's already got the record. Her handbag is held up high enough to be in front of her blouse's buttons in the first shot, but not visible at all in the next close-up. (00:36:30)
Answer: It helps him create a tolerance for pain. As we see, he certainly gets a lot of that dished out to him.