Continuity mistake: Towards the end, when Tim Robbins is chasing the President's car, he stops by Einstein's house first (he is wearing a red jacket). When they show a close up of his hand knocking on the door, his sleeve is blue. When they cut back out, it's red.
Continuity mistake: When Tim Robbins and Meg Ryan are on the balcony looking at the stars, the camera is doing a shot from the front - Tim is on the right and Meg is on the left. The camera then does a shot from behind them and Tim is still on the right and Meg is still on the left.