Second City - S1-E12
Deliberate mistake: Kermani finds a nitroglycerin tablet in the suspect's apartment. Because we need to see it when he holds it for the close-up, the tablet he has is much too large to be nitro. That drug is dispensed as an extremely tiny pill designed to dissolve instantly under the tongue. (00:22:30)
Deliberate mistake: Here, as in many other episodes, Doug and Tony are time-shifted wearing period (in this case, Viking) clothing. But they tumble into their next adventure magically wearing their left-behind 20th Century clothes again. (00:45:30)
Suggested correction: A comment, not a correction to your astute and correct observation about the Time Tunnel. Aside from it being episodic television that allows characters to look the same in all situations, I believe Tony and Doug keep their clothing, hair length, lack of facial hair, etc, because the Time Tunnel "remembered" the exact disposition of Tony and Doug when they first entered the Tunnel, allowing them to keep their clothing, hair length, etc., as they slip through time. Any "Time Tunnel" aficionados wishing to add more to this would make a fascinating discussion.
A valid speculation with which I agree, but as the poster himself points out, not a correction.
Deliberate mistake: On several occasions throughout both series/seasons, whenever a Terminator fires a weapon, they blink. This should not happen because that would be a human reaction - Terminators aren't human. They're made to look and act human, but SkyNet don't focus on the little things; such as emotions, breathing and reflexes. The three most notable instances of this are in Season 1, Episode 5: "Queen's Gambit", Season 2, Episode 21: "Adam Raised a Cain" and Season 2, Episode 22: "Born to Run". In "Queen's Gambit", Cameron blinks as she fires a machine gun at the T-888 in the back of the black van as he runs towards her, in "Adam Raised a Cain" the water delivery Terminator blinks as he shoots Savannah Weaver's nanny Debbie and as he shoots the security guard and Catherine Weaver in "Born to Run".
Deliberate mistake: When Wonder Woman is bouncing around in the padded room, there's one part where you can tell the stunt double is not Wonder Woman.
Deliberate mistake: As the Wraith "stun bomb" activates at the SGC and everyone falls to the ground, it is visible how everyone uses their arms to dampen the fall.
Deliberate mistake: Several shots have been taken from Series 1, including the group of guards firing in the hangar bay, and various shots of the shuttles during the chase.
Deliberate mistake: When the T-Ship is hit from the blast from the exploding space station, it spins around for a while before it re-stabilizes. Just before it does so, look out of Raven's canopy: the background outside with the stars and even a planet spin as the ship does, whereas realistically it should remain calm and stable.
What If... Captain Carter Were the First Avenger? - S1-E1
Deliberate mistake: When Peggy and Steve are studying the map where the 107th Army division is held captive, the names on the map are nonsensical names that do not even follow German spelling or standards for place names ("Farfignugen," "Dädtenorth," and "Rosskjhberg," for instance). Most of them are also reused, appearing several times on the same map. This is most likely done deliberately so as to avoid any resemblance to real places, but still looks out of place and illogical. (00:11:27)
Deliberate mistake: In the scene when the timer exceeds 38 minutes, said timer is displayed in big digits on a computer screen. There is a shot of General Hammond with the Stargate in the background. There is a pane of glass between the General and the Stargate. In the shot, General Hammond turns and looks at the gate, and then the camera's focus changes from the General to the Stargate itself. In doing so, a reflection of the timer in the pane of glass is also brought into focus. However the timer is displayed correctly when it should be flipped left to right as all text is when it is reflected in either a pane of glass or a mirror. On the DVD, the writers revealed that this was done on purpose so that the viewer would have a concept of the time running out even when the timer wasn't in shot. (00:17:30)
Deliberate mistake: Towards the end, Logan is thinking about killing himself and the water drips from the ceiling. He is on the top floor, so nobody would be living above him.
Deliberate mistake: Season 2, episode 6 "Identity Crisis": When Bizarro starts decaying into the parody form of Superman, his costume goes with it; the blue fades, and even the 'S' insignia changes. Strange that superhero garments change right alongside their wearers when they suffer from an unstable genetic effect. Were the clothes cloned right onto his body, instead of sewn?
Crisis on Earth-X, Part 2 - S6-E8
Deliberate mistake: During the big battle, Arrow is knocked down and when he opens his eyes, the reflection in his eyes is tilted over to give the sense he's seeing things sideways. But the reflection should still have shown the proper orientation no matter what orientation his eye was at. Think of looking into a mirror and then rotating the mirror to the side, the reflection wouldn't rotate.
Deliberate mistake: At the very end, Tommy And Merton discover the video tape which contain pictures of Merton that had been film by her sister Beckie, but the movie was filmed and the time ''rewind'' because of the spell. So in reality, the movie was never filmed.
The Garden of Evil Affair - S1-E8
Deliberate mistake: The bad guys chase Mark through a movie studio backlot past a London bus with a large red "Out of Service" sign on its side. During the ensuing shoot-out scene, the film is reversed for some reason, and the sign on the bus is suddenly backwards. (00:24:20)
Deliberate mistake: The police car Steve & Danny are driving on the bridge as they approach the freighter has 467 on the roof, which then becomes flipped & backwards a few shots later as they take a sharp right, only to become 467 again (as Danny has conversation with Rachel). (00:38:10 - 00:39:05)
Deliberate mistake: In the episode "Bunk," a man goes in the house looking for his cat. When the cat releases the fumes, it jumps down, but when the man dies, the cat is nowhere to be found. The cat is not mentioned ever again in the episode either.
Deliberate mistake: *SPOILER ALERT* Behind T-Bag is the actor who plays Lechero, and Lechero had just died in the episode. The person was not Lechero, but maybe they didn't have another extra at hand to replace him. 'Time 1' and 'Time 2' are taken from Netflix at the time this was posted. (00:29:46 - 00:30:25)
Deliberate mistake: Because the series changed networks after the end of season one, this episode completely ignores that season's cliffhanger about Harm being arrested as a suspect in the murder of Lt. Schonke.
Deliberate mistake: In the butter skating scene, the boys signing Paisley's cast are not writing anything. They are just pretending and their pens don't even touch her cast.
The Pieces of Fate Affair - S3-E23
Deliberate mistake: Because lawyers for real-life review columnist Judith Merrill were not amused by the parody of her and sued, the name Judith Merle is very obviously dubbed over throughout the episode (and changed in the credits) to Jody Moore. (00:32:50)