Deliberate mistake: Many of the Rangers in the Legendary Battle could not be there since they were portrayed by the same person. All 3 Rockys, all 3 Adams, and both Jasons and Kimberlys were all present.
The Night of the Tottering Tontine - S2-E16
Deliberate mistake: The knife that has just killed one of the investors doesn't have a trace of blood on it. No one had time to clean it off. (00:20:00)
The Defection of Hawkeye - S1-E8
Deliberate mistake: When Mandarin is watching and wondering why Julia is tailing Clint, the road surface and cliff walls around Julia's car are recycled repeatedly. (00:10:55)
Deliberate mistake: When the show premiered on March 18th, 1981 Ralph's last name started out as Hinkley, but after a couple of episodes had aired on TV, on March 30th a man named Hinckley shot then U.S. President Reagan and three other people, so in the remaining episodes of season 1 Ralph's last name was changed to Hanley. His last name was changed back to Hinkley in season 2.
Winning Through Intimidation - S1-E15
Deliberate mistake: In the actual card game, attacking the castle ring would not be allowed, but this is probably done in order to enhance the show for kids.
Night of the Sentinels: Part 1 - S1-E1
Deliberate mistake: When the Sentinel is first walking through the mall, its footsteps are so heavy that it shakes the building. When it is shown walking past the shop Gambit is in, there is no shaking of the building, presumably done so Gambit wouldn't notice it. (00:04:08)
Deliberate mistake: Inside the home that has been infested with Evil, the state police confront a possessed girl who attacks them. After some futile gunfire, the possessed girl is still standing. The female officer goes for her backup gun, which for some reason is a small over-and-under Derringer (meaning she has two shots maximum). She ends up firing the Derringer five times in just a few seconds, with explosive damage and without reloading. Director Sam Raimi probably staged the 5 gunshots on purpose, knowing that a two-round Derringer was a ridiculously-limited piece of firepower. Raimi probably did this as a tongue-in-cheek tribute to Ash's bottomless double-barrelled shotgun from Evil Dead 2 and Army of Darkness.
Deliberate mistake: The last season touched on Infinity War happening - this season jumps forwards a year, meaning that we should be one year into the "blip" (or snap), with half the universe missing. But The Team is all together, and the world/universe is utterly unaffected. Largely a byproduct of disagreement between the film and TV sides of Marvel, plus scheduling vagueness meaning they couldn't risk spoiling Endgame if they came back on the air before that was released. But considering the show is 100% part of the MCU, that's a pretty massive contradiction.
The Last Temptation of Barry Allen, Pt. 2 - S6-E8
Deliberate mistake: There's an awkward moment during Cecile and Kamilla's escape from Bloodwork's minions where Cecile doesn't close the door for several seconds so the cameraman can walk through as they follow them.
Genesis (2) - September 13, 1956 - S1-E2
Deliberate mistake: When Sam ejects and lands on the ground, the closeup is a flipped shot, note the "US Air Force" is backwards on Sam's helmet. (00:19:10)
Deliberate mistake: When the turtles and April escape the building filling up with water, the shot where the hall is filling up with water is used twice.
Deliberate mistake: During the episode, whenever daily newspapers are shown, they lack any indication of the date.
Deliberate mistake: Probably best for filming the scene, but Jennifer Hart pulls up and parks her car on the street on a red curb in front of an ambulance and walks away. (00:10:12)
Episode XCII - S5-E1
Deliberate mistake: Jack stops his motorbike beside a stream, and Jack's weapon strap crosses over his left shoulder when he walks over to have a drink. The problem is when we see Jack's reflection in the water, his image is not reversed; note the strap is still crossing over Jack's left shoulder. (00:07:20)
Deliberate mistake: At Pete's diner, the owner puts the tray down, and instantly glasses appear in front of the 5 patrons. (00:02:50)
Deliberate mistake: When the sewer worker is trying to escape the Lizard, the fast lanes in both directions of traffic are visibly clear for several blocks, which is extremely unlikely in downtown New York. (00:01:10)
Deliberate mistake: Throughout the episode, all the police station clocks are still and show the same time (3:33) in different scenes. (00:18:55)
Deliberate mistake: As usual when the Hulk reverts back into Bruce Banner, he is left wearing nothing but tattered pants. When Mitch McCutcheon sneaks Bruce Banner into the nuclear research facility, Banner is shown wearing his usual outfit of a gray collared shirt tucked into purple slacks that are intact. Given that the Hulk was just in the middle of the Nevada desert, Bruce Banner would be in no position to have a change of clothes on him, and the idea that the top secret facility would have an exact match of his go-to outfit is ludicrous.
Deliberate mistake: The Seal takes a shot with his suppressed pistol through a circular window in the hull of the ship at a hostage taker holding a hostage. When he fires through the glass it never breaks or shatters. Makes no sense how the bullet even passed through. In addition, windows in ships are really thick; it would've taken a few shots to get through and to neutralize the hostage taker. (00:33:30 - 00:34:30)