Revealing mistake: After Rygel realizes that he can loosen the soil with the dumped gruel, it cuts to John and Aeryn as they approach the Tavlek camp, and when Aeryn tells John, "I am going to take out every last Tavlek. No survivors. No mercy. Now give me the oculars," John holds up the syringe (with Zhaan's sleep mist) that Aeryn had given him earlier, and we can see "DG-4" engraved on the side of the gun, revealing that the prop dept used the model DG-4 aluminum air blow dust gun to play the part of the syringe.
Revealing mistake: When the shrink locks the door on Tony, they argue and she calls the police. When she finally calms down she approaches the door to unlock it but you can see the door move before she ever sticks a key in it or touches the knob. (00:25:20)
Revealing mistake: After the fight between Stewie and Olivia at the concert hall (followed by their breakup), Simon tells Stewie that the act without Olivia is "over" as he turns to walk off the screen. However, before Simon is even partially out of the shot, he completely disappears. (00:18:45)
Revealing mistake: When Amanda and Fin are in Atlanta following up on their rape case, they walk past several cars with visible Georgia license plates mounted on the front. Georgia is a rear plate-only state and wouldn't have had license plates mounted on the front of the cars, as shown here. (00:13:30 - 00:16:20)
Revealing mistake: Oliver Babish's office has windows in a location it can not possibly have them. Jed and Leo are in continuous conversation as they leave the 'normal' West Wing set at the end of a hall (See http://www.whitehousemuseum.org/special/wwtv.htm where the words 'Press Briefing Room' are - that's where they turn to their right). They walk a few steps then turn right again and ahead of them is Babish's office, with windows straight ahead. If this had been a single continuous set, Babish's office would be located in the stair area to the left of the press briefing room, and the windows would offer a view of the hallway that runs between the lower corners of Leo and C.J.'s offices (seen at 3:36), not the outside world. (00:03:30)