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: While De Niro is talking to Jodie Foster you can see a bus out the window. When the screen switches to Jodie Foster's view you can see the same bus driving, but then it changes back to De Niro's view you see the same bus driving up to the window again. This keeps happening throughout the scene, the bus keeps driving around the building. (01:27:00)
Continuity mistake: When Robert De Niro shoots the pimp's hand off in the hallway (shortly before shooting Sport the second time), blood splatters on his face, across his left eye and forehead. As he stumbles up the stairs (still shooting the handless pimp), the blood has changed, and finally in the shot where De Niro pantomimes shooting himself, the only blood on his face is on his chin. (01:39:40 - 01:42:40)
Other mistake: Travis' hair length appears inconsistent throughout the movie; he begins working in early May with his hair of a certain length, his hair appears trimmed differently in certain scenes driving the cab, it is certainly much shorter, sort of a buzz cut, during the scenes when he interacts with the senator's guards, but it is already longer when he is doing the "You talkin' to me scene" and the murder of Stick-Up Man, which is in between the buzzcut scenes. And then of course, there's the ending.
Visible crew/equipment: In the scene where Robert De Niro shoots Sport the pimp in the stomach, the bullet supposedly goes through Sport's back, and blood splatters onto the doorway framework behind him. However, as Sport falls to the ground, look closely, and you can see a wire dangling from his lower back, which was used by the special effects team to detonate the fake blood packet. (01:39:05)
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)
Continuity mistake: In the scene where the man has DeNiro pull over to the curb and says he is going to kill his wife with a .44 gun, there is a close up of the meter clicking over to $2.75. In the next shot from the backseat, the meter reads $0.65.
Continuity mistake: During the fight in the end, Travis shoots a man's hand and his four fingers are blown apart; yet when the same man jumps at Travis as he enters Jodie Foster's room, you can briefly see two of his "missing" fingers on Travis' shoulder. (01:39:40)
Continuity mistake: In the scene where De Niro shoots and kills the man robbing the convenience store, the clerk takes De Niro's gun off of him and starts beating the already dead body with a pole. If you watch the scene carefully, the dead body changes positions contrary to how the man is hitting him. Clearly the scene was shot several times with the dead body being placed in different positions. (01:09:40)
Other mistake: There seems to be no bullet impact into the wall or near Murray Moston after the .44 Magnum revolver is discharged. Given the general direction and angle the weapon was pointed, a bullet should have blown out part of the wall near Murray Moston.
Continuity mistake: During the same scene there is a white van parked across the street behind De Niro. Then it's gone. Then it's back.
Character mistake: When Travis is buying guns, Easy Andy (the gun salesman) makes a few errors. Firstly, he states that the Smith and Wesson 61 Escort is a "Colt .25 Automatic." Secondly, he calls the Astra Constable a ".380 Walther." And lastly, he talks about the ".380 Walther" saying "during World War II, they used this gun to replace the P38. Just given out to officers." This is also incorrect.
Factual error: Travis begins the movie at 26 years old, and reports leaving the army with honorable discharge in May 1973. His first diary entry just after being hired is "May 10th." In the newspapers at the end he is still 26, and it says that he has been a taxi driver for 6 months. The movie obviously does not take place in winter, and the only months referenced (plus the timeline of a presidential nomination) are June and July. Besides, 1973 would not be the right year for a story set just before a presidential election, unlike 1976 when the movie came out.