The Killer - S1-E1
Continuity mistake: At the beginning of the episode, The Killer (John de Lancie) strikes. He is holding the champagne flute with the middle finger curled between the hand and the belly of the glass, but in close-up the finger is at a right angle in front of the stem. (00:01:55)
The Killer - S1-E1
Continuity mistake: Jim's pupil and successor Copperfield is poisoned at the beginning of the episode. He screams, drawing the attention of the party guests. In the following POV shot, the guests are standing in entirely different spots in the room all of a sudden. (00:02:45)
The Killer - S1-E1
Continuity mistake: When Jim picks up the box with the mission briefing, his hand in the close-up of the fisherman's case is at the bottom of the box, but it's on the opposite side when we see Peter Graves retrieve it. (00:07:00)
The System - S1-E2
Continuity mistake: Jim approaches the secret agent on the usual convoluted way to the mission briefing. The peanut vendor mentions the quarterback, and behind him there is a person walking in the tunnel. Switch to a new shot and there are two. (00:02:40)
The System - S1-E2
Continuity mistake: Grant begins to remove the screws from the vent starting from the right side, but the top row is already missing and unscrewing 2 on a single side already makes the vent wobble significantly before the camera cuts away. (00:14:00)
The System - S1-E2
Continuity mistake: Casey is having a chit-chat with the villain/stooge of the episode, playing dumb and pretending to have a ridiculous 'system'. As she says that whenever she loses she doubles the bet "three times in a row", her hair goes from behind the shoulder to the front of the shoulder. (00:16:05)
The System - S1-E2
Continuity mistake: When Nicholas distracts Chuck the security guard with a phone call (terrible plan, since he tells him to search in a spot awfully close to the monitor he's supposed to be distracted from), he touches the papers next to the monitor and the pen in front of it, but when it cuts to him looking at the recording while Grant is working the safe, the objects are in the exact same position as before when he was looking at the money count. (00:19:55 - 00:26:15)