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.
Dale Cooper's role was originally larger than it appeared in the final film. Kyle MacLachlan had originally declined to appear, for fear of being typecast. To compensate, his role was downgraded to a minor cameo, and a new character was created to fill the role of lead investigator.