Continuity: 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.

Continuity: 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.