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.
Deliberate mistake: When the chickens are first shown, one of them is upside down.
Deliberate mistake: Every time the commandos are seen in the early episodes of this season (The Freshman and Fear, Itself) they wear ski masks to protect their identities. Starting in The Initiative, they stop doing this. The reason is that the audience needs to be able to identify the different commando characters, but it's still a discontinuity.
Deliberate mistake: The dying Vantika hides his consciousness away in a portion of Dr. Bashir's mind. At one point, "Bashir" (heavily cloaked in clothing and shadows) comes up behind Quark and makes sure his demands are clear. At this point, it should still be unclear just how Vantika is still "alive", and whose body he is using. However, when he shoves Quark away, for a fraction of a second, Bashir's face can be seen under his hood. They were true to plot in using the right actor (though he shouldn't have been seen), it is possible some might have spied the secret earlier than the show meant to reveal it.
Deliberate mistake: At the beginning, Asajj Ventress is wearing an outfit with a long skirt. When she is rescued from her damaged starfighter by the scavengers, the skirt has vanished. This was done because the animators found the skirt too difficult to animate. This is also why she receives a brand new outfit that never had a long skirt later in the episode. (00:08:20)
Deliberate mistake: When Johnny is watching the news footage of the Hulk battling Thing, all the footage is merely clips from that portion of the episode, including parts of the battle that were happening before the camera crews even showed up. (00:02:50 - 00:07:20)
Deliberate mistake: Although it is later revealed that Sarah is the intruder, the person fighting is male.
Deliberate mistake: In fight scenes, the Yellow Ranger's stature matches that of a male (and not Trini). This is because in the Japanese version of the show, the Yellow Ranger was played by a man.
Deliberate mistake: Rampart's ER is located in the south lower wing of the hospital complex and it is only a two-storey building (with a basement), but the elevator, which is located past the nurses' station at the wing's far south end, has two floor indicator panels listing eight floors - one panel over the elevator doors and another we see every time the elevator doors open, which is not possible.
Saga of a Star World (1) - S1-E1
Deliberate mistake: When the large formation of Cylons attack, the graphic that Athena is looking at shows the approaching Cylon ships as triangles, as usual. But it also shows two asterisks leading that formation, and the asterisk is the symbol for Vipers. There are NO Vipers leading the Cylons in this sequence. This graphic is a reuse of the one from the big battle at the start of the episode when Apollo and Zac were being pursued by an earlier large formation of Cylons. (02:00:30)
Day 2: 6:00 P.M.-7:00 P.M. - S2-E11
Deliberate mistake: When Jack and that FBI team are looking for Sied Ali in the mosque, Jack finds a burning body in another room. He is led to believe that it is Ali, because the body's clothes matched the description that Kate Warner had given him. It is obvious that the skin is badly burnt, yet the clothes are barely scorched.
Slammin' Sammy's Stunt Show Spectacular - S1-E5
Deliberate mistake: Watch the end of the test run for Michael and KITT. Michael was using the KITT steering wheel, but then he gets out of the car and it switches to a performance steering wheel instead.
Deliberate mistake: Though he moved freely about the station in his environmental suit, Kosh was never actually seen going through a door. He approached doors, but then, sometimes rather disconcertingly, would suddenly be shown on the other side. The reason: look closely and you'll realise his costume was too large to fit through any of the doorways on the set, so in reality the character would never have been able to move around the station.
Honey, I Shrunk the Rangers: Part 1 - S1-E16
Deliberate mistake: Monkey Bulk & Skull are driving Lt. Stone's car. From inside shots of the car, Monkey Bulk's head doesn't go above the headrest. From outside shots, we can see the guy who was driving the car - his head is way above the headrest, and he's wearing a frizzy fur costume (Monkey Bulk & Skull's fur is very fine).
Deliberate mistake: At the beginning of the chapter, as the scene switches to the surface fighting on Muunilinst, we see a score of droids blasted before the Republic Army's heavy artillery is brought in. But there are no remains on the droids to be seen after the smoke has cleared, whereas there should be something left.
Deliberate mistake: When Sixsix impacts with the ground due to Greymatter sabotaging his jet pack, the furrow he ploughs into the ground is already present when he skips across the ground.
Smack in the Middle (2) - S1-E2
Deliberate mistake: Ignoring that its very unlikely all of Jill St. John's copious red hair would fit under a wig that passes for Robin's hair, it's impossible that it would emerge from under that wig looking as full and perfectly styled as it does when she's in the Batcave.
Deliberate mistake: In the flashback to Angelus rising from his grave, his and Darla's breath is visible as they exhale. This was going to be removed in post-production, but left in due to budget restrictions.
Deliberate mistake: When one of the yellow fire trucks moves away from the burning Thompson Tower, the back of the truck is set alight by the flames.
Yankee White - S1-E1
Deliberate mistake: Fornell doesn't recognize Gibbs, but subsequent episodes establish they have a long history together.