Trivia: Director Martin Scorsese makes more then just a cameo in this film, he's the passenger that sits with Travis talking about how he's going to kill his wife for cheating on him with a black man. He's credited as "Man Watching Silhouette".
Revealing mistake: When De Niro gets shot in the neck, his bald skin cap wrinkles considerably when he presses the wound with his hand. Confirmed by make-up artist Dick Smith in the making-of documentary. (01:40:00)
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)
Visible crew/equipment: Right before De Niro's character is shot in the neck, you can see the small charge used to detonate the blood. (01:39:50)
Continuity mistake: Taking a fatal bullet from Travis, the robber falls back. He is not just breaking the snack display cabinet, but also knocking one of the dirty Spanish magazines off the clothesline. The magazine falls with him and gets all crimpled between his arm and the counter, but vanishes entirely in the rest of the scene. (01:08:50)
Revealing mistake: When the Senator finishes his speech and steps off the stage, Travis begins to move making his way through the crowd. Several extras are recycled appearing in inconsistent positions - look no further than the black woman with a bright flower patterned pink shirt; she is simultaneously in front of Travis as he begins to move in the outer section, and right between Charles Palantine and the stage in the shot immediately after. And then she keeps popping up where she's not supposed to be, continuously. (01:36:20)
Continuity mistake: When the store owner beats the carcass of the robber, Travis' pistol is either to the right of the box on the counter or to the left, together with the gun of the robber. (01:09:30)
Continuity mistake: The breakfast scene ends with Jodie Foster having a bunch more toast on her plate than at the start. (01:26:40 - 01:29:20)
Revealing mistake: When Travis starts spelling his phony name out to the security guy, a ginger kid walks in, stares at the camera, and hides away as quick as he came. In similar fashion, another kid with a red baseball cap looks at the camera behind De Niro once this walks by evading the photographer. (01:04:20)
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)
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).