Episode Nine - S2-E2
Continuity mistake: The necklace James took from the coconut in Dr. Jacobi's office in the previous episode had a gold chain. When he gives it to Agent Cooper in this episode, it's on leather.
Revealing mistake: When Leland Palmer is locked in the cell he starts screaming and runs headlong into one wall, then the other. The first wall wobbles noticeably on impact, indicating it is being shot on a set.
Visible crew/equipment: When Audrey enters her father's office to find him in the middle of his Civil War recreation, a boom mic dips into the shot over their heads. (00:18:40)
Plot hole: In the bait and switch section, why does anyone involved agree to Leland being Ben's attorney when both victims are relatives of Leland? Neither Ben nor any of the police are in on Cooper's plan, and it seems implausible at best that they would agree to this.
Character mistake: At the Roadhouse Cooper states that the second victim (Maddy) was found dead two days ago. It has been less than 24 hours since the body was found: he likely means she was murdered two days ago.
Continuity mistake: At One Eyed Jack's, when Agent Cooper and Jacques are sitting and talking there are 2 glasses of beer on the table. In one shot Jacques finishes a glass. When he gets up, both glasses are full. (00:10:20 - 00:11:40)
Visible crew/equipment: When Sheriff Harry S. Truman first leaves the station, film crew are visible as they dolly back across the Ford Bronco. (00:05:55)
Visible crew/equipment: When James and Maddie meet by the lake, a clear blue trail of cigarette smoke flows in from the right, it's most probably someone's smoke from the crew.
Continuity mistake: In the hotel lobby, the chair that Leland knocks over switches between shots between lying on its side and on its back.
Continuity mistake: The plate, bread and milk that Pete drops on the floor change position between shots.
Plot hole: Harry states that Ben was not arrested until after midnight. However in episode 2.7, the arrest takes place earlier in the evening, shown in establishing shots and the other events which occur afterwards.
Visible crew/equipment: At the very end, Sarah is alone while she's lying down, but when she has the sudden vision of Laura's necklace being dug up, the reflection of a crew member is visible in the round mirror. (01:32:50)
Continuity mistake: At about 23:21, Dale Cooper is writing on a chalkboard that has the letters R and T on it, not circled. Moments later, at 23:30, the letters are circled, even though Cooper has not marked the board. (00:23:20)
Suggested correction: Actually, there is a cutaway shot to the two policemen, and when the shot changes back to Cooper (with the letters now circled, as you say), he does have the chalk in his hand and then circles the "J." I think it's implied he circled the R and T in the cutaway. There was enough time.
Other mistake: When Cooper is on the floor after being shot, as he's signing the check, he is doing so with the pen closed, and proceeds to click it open as he hands it back to the room service.
Continuity mistake: Nadine decides to lift leg weights beside Mike. She sets it to 600 pounds. However, whenever it changes view to her lifting from the angle of Mike, whenever the coach asks her to join the team, you can see that Nadine is not lifting any weights. (00:19:45)
Visible crew/equipment: When Josie and Catherine are arguing at the mill, just as Pete says, "Oh Catherine, please," he moves toward the chair, and the reflection of a crew member wearing a cap is visible on the window, at the left side of the screen. (00:32:25)
Visible crew/equipment: When Truman brings Leland to the hospital for confirmation on the body's identity, the attendant turns on the overhead light, then takes a step back, and the actor's tape mark is visible on the floor by his feet. (00:19:40)
Visible crew/equipment: While Truman and Cooper are at the bank, when they take the safety deposit box and walk over to the table, there's a green tape mark on the floor by Truman's feet. (01:03:20)
Episode Six - S1-E6
Visible crew/equipment: When the lawyer goes to leave, after discussing the life insurance policies with Catherine Martell, a boom pole is visible moving in the window reflection behind Catherine. (00:29:03)
Episode Six - S1-E6
Visible crew/equipment: When Hank steals the lighter at the diner, his and Shelly's previous tape marks are visible on the floor behind him. (00:17:40)