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: 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: 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: 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: 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: The guns Travis purchases from Easy Andy are (regardless of what Andy calls them), from left to right, a Smith and Wesson Model 29, a Smith and Wesson Model 36, a Smith and Wesson Escort, an Astra Constable. In the overhead shots at the gun range when Travis goes to practice immediately after, some of the guns change: the first 44 Magnum is the same, but the 38 becomes a Colt Detective Special, the S&W Escort a Galesi-Brescia Brevetto 5, the Astra a Walther PPK (which is what Andy called it earlier).
Continuity mistake: Travis Bickle is preparing for his mission. He puts the flowers in the sink and burns them, he cuts one sleeve from his shirt so he can accommodate a special retractable holster, and then...then he is writing a note for Iris, wearing a shirt with both sleeves, in a room still full of wilted flowers. (01:33:00)