Continuity mistake: When Harry and Lloyd are leaving Providence, in the first shot of the highway we see them driving on Route 146. In the next shot showing the Highway, they are driving on Route 95 South. There is no way they can be driving on both highways at the same time, and, if they could, they would be driving in opposite directions at the same time.
Other mistake: In the brief scene in which Nicholas Andre and J.P. Shay are talking about the killing of the owl at the preservation society ball, if you look very closely out the very bottom of the window, at the very end of the short scene (right after Andre says, "Their guys aren't just anybody, they're good"), you can catch a brief glimpse of part of the box containing the victim who is trying to escape (this box was completely excluded from the film).
Continuity mistake: After Harry and Lloyd start gagging over the atomic peppers, we see a brief shot in which everyone else in the restaurant looks at them (and the waitress suddenly appears in that shot as well). But in very the next shot (back to Harry and Lloyd, still gagging), nobody is looking at them (and the waitress, who was there just a moment ago, disappears).
Continuity mistake: When the "gas man" falls to the floor due to the atomic peppers that Harry and Lloyd sneaked into his burger, Harry and Lloyd laugh at him, and Lloyd even points at him. Then he stops pointing at him and looks at Harry. But only a moment later, in the very beginning of the next shot (a close-up of Harry and Lloyd), Lloyd is instantly pointing again.