Continuity mistake: When Agent Desmond is waiting to see Sheriff Cable, the position of the hand supporting his face changes between shots. (00:08:00)
Continuity mistake: When Chet and Stanley asks Irene some questions (in the café, about 15 minutes into the movie) about the murder, the cigarette Irene smokes changes a few times between the shots. Most obvious is the length of the ashes. (00:16:13)
Character mistake: Leland Palmer handles Laura's body without any gloves when wrapping her and disposing of the body. As with any respectable FBI investigation, upon finding her body and checking for fingerprints, they should've connected Leland to Laura's death within days. (02:05:00)
Continuity mistake: When Ronnette and Laura are in the cabin with Jacques and Leo, Ronnette is wearing sheer pantyhose - her legs shine in the available light - and this is more obvious when Jacques cops a feel of her legs. The last time we see her in the movie she drops out of the train car, still wearing them. (This happens 8 minutes from the ending credits.) But when she was first shown in the series "Twin Peaks" (we see her walking on the train track) she was not wearing pantyhose.