Continuity mistake: After applying for his job, Travis walks towards the exit of the garage, jacket unzipped. In the next shot, the passersby change and his jacket is zipped 1/3 way. (00:04:35)
Other mistake: When the woman at the theater gives Travis his Cola, she never pours it. (00:09:25)
Continuity mistake: Travis is at the concession stand of the theater and has all his candy bars on the counter. Even after he draws the popcorn in, the bars are off the mag the dismissive cashier is reading. She reaches for the cheap cola she somehow manages to pour, and when she puts it with Travis' stuff the magazine is open at a different page and the candy is on top of it. (00:09:25)
Continuity mistake: When Betsy is pointing the taxi driver outside to Albert Brooks, both her hands and his change position in the next shot, when he asks if the cabbie stalker is bothering her. (00:12:55)
Continuity mistake: In the first scene with the fellow cabbies at the diners, Wizard introduces Doughboy and Charlie T to Travis. Charlie in the very first shot has his toothpick on the right corner of the mouth, but in the close-up it is all the way to the left. (00:16:00)
Continuity mistake: In the scene at the diner, where Travis puts a soluble tablet in a glass of water, you can see a plate of open cheeseburger in front of him. But Travis never ordered, nor received any cheeseburgers. He only ordered and received a cup of coffee only. (00:17:10)
Continuity mistake: When Betsy pranks Tom with the paper cup, she 'spills' it with the right hand in the front view, and holds it in her left hand in the reverse shot. She then lifts it well above shoulder level and turns it upside down to show that it is empty, but in the next shot it is at the same height and angle as before. (00:18:25)
Continuity mistake: In the last part of the 'stool pigeon' bit between Cybill Shepherd and Albert Brooks, the paper sheet rolled in the typewriter has moved without Tom operating the device at all between shots. His hands also change position between shots (for instance, he points his finger with both hands joined at first, but at the cut just one is raised). (00:19:50)
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: During the chat the protagonist and Cybil Shepherd have at the diner, the passersby outside often walk back and forth. Easily recognizable for instance a redhead with a white shirt, blue skirt and a red ribbon tie, a woman with a blue tee and grey hair, another one in a pink tailleur and straw hat, and many more. (00:23:30)
Continuity mistake: Travis and Betsy are having their snack during her break. During the conversation there are several instances when vehicles you can spot through the window behind De Niro do not move to Cybil Shepherd's side, or vice versa suddenly show up behind her appearing out of nothing. For instance when he says he says "quite a few problems" the orange car does not travel in between shots, and then a taxi appears behind her. Then there's a bus behind him which is suddenly gone between shots, etc. (00:25:00)
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: 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)
Continuity mistake: The close-up of the taxi fare meter during the scene with Martin Scorsese's cameo has lighting inconsistent with the rest of the scene. (00:41:00)
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: 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: 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: 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)
Visible crew/equipment: In the scene right after DeNiro is watching the Senator on the TV, he is driving in his cab past the campaign headquarters. As the camera goes past the window and focuses on desk phone, you can see the reflection of a cameraman for a second or so in the glass. (00:51:00)
Answer: This is just my opinion. Remember Iris's line "Have you ever tried looking at your own eyeballs in the mirror?" or something to that effect. Well, Travis sees the madness reflected in his own eyes, doesn't like what he sees (as it reminds him of what he has done, what he might yet do).