Continuity mistake: In the scene on the Strip where Gonzo is vomiting out of the car and yelling abuse at the couple in the adjacent car, he vomits on the other car's window. After this, no vomit is visible on the window in shots from inside the other car. When shot from outside, the vomit is still there.
Continuity mistake: After the Vegas Hotel check in, Duke bums a light off a dude in the bar. At first the cigarette is broken and lit, then the broken piece falls onto the ground during the bloody floor sequence. As he turns full circle in his chair, the cigarette is back to its broken state again, then after a shot cut, it appears to have lost its broken tip again, without any loss in cigarette size.
Continuity mistake: When Gonzo offers the hitchhiker a joint, there is a cassette player on the seat between him and Duke. A couple shots later Gonzo swerves in the road, and when Duke hits his headrest there is a brown briefcase next to Gonzo on top of the player. In the next shot Gonzo reaches into the back of the car get the briefcase.
Continuity mistake: When the Duke and Gonzo are driving to Vegas in the beginning, they debate whether to pick up the hitchhiker. They drive past him and then about 10 seconds later decide to stop. But when they finally stop and the camera pans back, they are only like 10 feet from they guy. Since you know they were speeding, they should have been like 1/4 mile past him by then.