Continuity mistake: In the scene where William Fichtner is shown first leaving his trailer and picking up litter in the amusement park, his gloved hand switches from his right hand to his left then back to his right again before he starts talking to the couple. (00:05:40)
Revealing mistake: As the gang drives up to the space-ship diner, cars are whizzing by in the background. When they are driving to the base there's also a clip of a fire truck going down the highway in the distance.
Other mistake: When McNulty uses the stopwatch to rob a bank, he goes through a small wooden door and past the employees. With time frozen, the small door should have stayed open but immediately swings shut.
Family Ties - S1-E22
Visible crew/equipment: After Rygel's transport pod returns to Moya, as the docking bay door slides open, in the shot facing everyone while they have their weapons drawn we can see the bare floor. However, when Aeryn checks Crais for hidden weapons and then as D'Argo approaches him, there's a blue crash mat on the floor. Then it vanishes again.
Broken Link - S4-E26
Revealing mistake: During the fight between Garak and Worf near the end of the episode, a Jefferies tube door is knocked out of its frame to reveal the end of the set - a dark room with a wooden scaffold and various other pieces of equipment (slow-mo helpful but not required). (00:36:00)
Other mistake: Right at the start, as they're crashing, the computer narrates their rapidly-dropping altitude in feet. But the "altitude" dial we're shown is in metres. Most noticeable as they cross the 3,000 mark, when the computer voice and the height say/show the same number at the same time, despite the different units. 3,000m would be more like 9,000 feet, or 3,000 feet would be more like 1,000m. (00:03:20)
Plot hole: In order to build up suspense, Virgil and Brains stand on the Crab Logger as its dangerous fuel is pumped out, despite the fact that it is hanging on the edge of a precipice. In fact they could have left as soon as they had plumbed in the pipes to empty the fuel tanks - the whole procedure is controlled by Scott in Thunderbird 1 and they make absolutely no contribution to the operation at all. They do not need to disconnect the pipes; they are left behind and dropped from Thunderbird 1 as planned. They just stand there chatting about how much danger they are in until jumping clear at the very last second. Silly buggers.
The Magician - S3-E4
Revealing mistake: When Oliver meets Thea at the Grind and Jot Cafe (Which looks unsurprisingly like CC Jitters) you can see the cups on the table are from CC Jitters. (00:20:50)
Visible crew/equipment: When Mulder and Scully enter the abandoned mine through a doorway, the viewer can see at right in the distance a number of people sitting on a wall, and one crouching in front of the wall with what looks like a dog. They are sitting still, but there is still movement there. (00:16:00)
The Night Dr. Loveless Died - S3-E4
Continuity mistake: In the opening scene, a cowboy sitting atop the balcony above Big Brad's Bar gets up and approaches the balcony's edge twice.
Free for All - S1-E4
Continuity mistake: Throughout the episode, Number 6's lapels switch from having solid to broken white piping and back again.
Kobol's Last Gleaming (2) - S1-E15
Visible crew/equipment: In the scene where Starbuck attempts to retrieve Apollo's arrow, a crewman in a red tee shirt and dark vest can be seen standing just behind and to the right of the display case as she is shooting out the glass.
Continuity mistake: When Charlie is climbing down the cliff the rope comes undone from the tree stump, but a few seconds later you see it still tied to the stump. (00:12:00 - 00:12:45)
Deliberate mistake: When the Doctor begins to "fade" in the transporter room his mobile emitter fades with him. Since it's made of solid matter and is not a hologram, this shouldn't be possible.
Factual error: In scenes from the oil rig there are shots that show the shore line. This oil rig is supposed to be offshore of Louisiana. However, mountains can be seen in the shots of the shoreline. There are no mountains in Louisiana.
Encounter at Farpoint (1) - S1-E1
Revealing mistake: When Q freezes Torres on the bridge, it is easy to tell that directional hoses were used for the effect. (00:06:25)