Factual error: The movie is set in 1971, but during the start of the motorcycle race several of the bikes are obviously early 90's Honda CR's and Suzuki RM's. You can tell this from the disc brakes on the front wheels of the bikes and the 90's style plastic fenders and bike colors. Bikes in the 70's generally had metal fenders and definitely no front disc brakes.
Visible crew/equipment: When the duo first enter the Vortex (the indoor circus place) they stop to look at themselves in the wobbly mirrors. The mirror also reflects the cameraman filming the scene. The image is distorted and upside down but he's definitely there and becomes clearer as the shot progresses.
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.
Visible crew/equipment: As the scene changes from Raoul Duke and Dr. Gonzo speeding to pick up all of the equipment for the photo shoot in Las Vegas to Dr. Gonzo talking on the payphone beside the aquarium, take a look at the reflection in the aquarium. If you look very carefully you can see a bald crewman dropping fish food into the tank, getting the fish to move with the camera towards Dr. Gonzo.
Continuity mistake: In the press tent, Depp's beer has some dribbling down the side of the glass. When the guy who asks him what day it is throws dust over Depp's glass, the dribble is suddenly gone. (00:25:10)
Continuity mistake: After they pick up the hitchhiker, Duke has a leather bag on his lap. In the shot when he turns around to talk to the hitchhiker he pushes it to the floor. In the next shot the bag on his lap and he pushes it to the floor to jump in the backseat. (00:04:53)
Continuity mistake: During the sentencing scene with Lucy, the flag moves from being to the right of her, then behind her head, then to the right of her again between takes. (01:24:35)
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. (00:04:48)
Continuity mistake: As Raoul is being chased by the highway cop, the camera switches views between the rear view and looking through the back window. The line in the middle of the road changes unevenly between passing and no passing lanes.
Plot hole: When Duke is being chased by the cop, Duke says, "But he won't know what to make of your blinker signal that says you are about to turn right. This is to let him know that you are pulling off for a proper place to talk. It'll take him a moment to realize he is about to make a 180 degree turn in speed. But you will be ready for him." Duke signals he is going to turn off to the right, but when he does, the cop turns to the left. (01:02:40)
Continuity mistake: When Gonzo is trying to kill himself in the bathroom, there's a watch behind him that appears and disappears between takes.
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.
Continuity mistake: When Duke and Gonzo are driving towards Vegas in the beginning of the movie, they pull over to pick up the hitch hiker. Gonzo puts the car in reverse and goes backwards really fast, but Duke is being pushed backwards against his chair!