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)
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)
Visible crew/equipment: When Palantine is walking through the crowd, several extra don't look at all where he is supposed to be, but at the camera, either staring directly at it breaking 4th wall when it's in De Niro's close-ups, or even more blatantly turning around (and away from the Senator) to look up where the camera crane is. (01:36:35)
Visible crew/equipment: Travis Bickle got all geared up to go kill the senator. There's an opening panning shot of Charles Palantine arriving at the location. As the relatively small scope of the meeting implies, but also as shown in the rest of the scene, there's no camera crew following Palantine, no big crane rig or anything. Yet you can easily spot people in this crowd who don't care about the Senator but look at the movie camera. One of the followers is particularly hilarious; on the left of the frame, he keeps waving his hand at the camera, tries to follow Palantine and direct the gesture at him, and then goes back to signaling the camera. (01:33:50)
Visible crew/equipment: Travis clears out because the policeman told him he can't park there and so he starts the car and drives. Everyone in the crowd looks (many turn around explicitly and ) as he passes by, in particular looking right where the camera car in front of the taxi is. The senator is supposed to talk in a different direction, where De Niro is looking. (01:12:55)
Answer: It helps him create a tolerance for pain. As we see, he certainly gets a lot of that dished out to him.