Continuity mistake: Colonel Gathers says to Brock Samson, "You're not in the Marines anymore." But in the earlier episode, "Past Tense," after the credits, there is a flashback to college again and Brock says, "I'm off to join the Army"
Revealing mistake: At the point where someone gets a small bruise on the upper arm, the crew are all in a pile and thrashing about on the floor. There are 5 pairs of legs instead of 4. Arthur is in his pajamas, Zaphod is in orange trousers, Trillion is lying on top of Ford and Ford is too far away for them to be his legs. [The fifth pair of legs belong to the person playing zaphod's third arm - doesn't mean it's not a mistake, but that's where they come from.]
Factual error: There is no physical way that Steve Austin could perform most of his superhuman feats of strength in the ABC television series, due to the fact that they simply replaced his arm and legs, but didn't rebuild or reinforce the rest of his skeleton and muscles to handle the physical loads. Interestingly, author Martin Caidin (creator of Steve Austin in his novel, "Cyborg") actually did describe an incredibly complex whole-body rebuild that included vertebral reinforcement and ribcage and pelvis replacement, which was far more scientifically-accurate than the subsequent ABC television interpretation. ABC only accepted the series on the condition that it was less technical for their audience.
Worlds Collide: Part 3 - S3-E6
Plot hole: In their previous encounters with the Triceratons, the Turtles had to learn the hard way that the Triceratons breathe not oxygen but a combination of nitrogen and sulfur, which is detrimental to most Earth lifeforms, and thus had to wear special rebreathers. When the Turtles, Splinter, April and Casey enter Zanramon's throne room along with Traximus, none of them wear any breathing equipment to protect themselves from the hostile atmosphere.
Other mistake: If you look closely at the army of Rangers in the opening credits, you can see four versions of Tommy Oliver: Green Ranger, White Ranger, Zeo Ranger Red, Black Dino Ranger. Even though he had a single clone made, he can't be four variations at the same time.
Character mistake: The Enterprise is targeted by projectiles from the planet. Spock identifies them as "plasma torpedoes", and Captain Pike reacts with surprise; "Plasma torpedoes? That's 21st century tech" and from that they all establish that the civilization they contacted is not yet capable of warp drive. Plasma torpedoes are the main weaponry of the Romulans centuries later, and Earth itself did acquire warp drive in the 21st century, so this claim and deduction don't seem to add up. (00:22:15)
Revealing mistake: The swords Jayden and Dekker use often bend when striking each other, revealing they are rubber blades and not metal.
Continuity mistake: The 4 Space Rangers (Carlos, TJ, Cassie, Ashley) morph on the overhanging gangway, then jump off to the ground below. We see them hit the ground, and in the very next shot, they're right next to the Galaxy Rangers, and Andross, who are on the other side of the courtyard. There wasn't enough time for them to move that distance.
Delenda Est - S3-E11
Revealing mistake: When Dylan and Tyr head to a bridge where supposedly the power source is located as well as Rommie, they start to cross the bridge. As the camera is facing Dylan and Tyr, the next scene two aliens teleport in. Rewind the video to facing Dylan and Tyr and play in slow motion. Watch the bottom portion of the screen and notice the top portion of one of the alien's head go into the camera as if the aliens walked into position for the teleportation.
Continuity mistake: The packages Drake and Kathy place on the table beside their coats have disappeared when they return for the coats a few shots later. (00:19:00 - 00:21:20)
Who Killed Avery Lord? - S1-E23
Visible crew/equipment: After the woman in the negligeé goes back into her apartment, a crew member's shadow appears on the corridor wall. (00:42:00)
Other mistake: When Jessica calls Hondo to let him know about Deacon's wife, you see Hondo answer the phone normally. Right after she tells him what's up, you can see him holding the phone upside down, with the camera lens towards the bottom. (00:24:30)
Character mistake: Dr. Agnes Jurati, one of the Federation leading scientists, is bored during the hyperspace travel, and so she chats a bit with the captain. While she gives her quirky speech, she casually mentions that "there are over 3 billion stars in our galaxy." She's not wrong, technically, but the number of stars in our galaxy is estimated between 100 and 400 billion. She is way off. (00:08:40)
Suggested correction: Two things. You state that she's not wrong, which she isn't. The fact that she chose an odd turn of phrase doesn't make it a mistake. Plus, you reference the number of 'galaxies' in our galaxy but I am guessing this is just a typo.
Beyond the Farthest Star - S1-E1
Other mistake: When showing Scotty on the bridge, some of the frames show more of his body than others. In those frames, you can see that he lacks legs.
Seeds + Permafrost + Feather - S3-E17
Factual error: Bozer and for that matter I would assume all of the team went to a spycraft academy. A basic subject in any of such academies is surveillance, including proper techniques to follow and stake out someone. Bozer being so inept at tracking MacGyver's father is inconceivable given their training.
Continuity mistake: Elisabeth Shue is talking to Homelander by her car. As she gets her baby out of the car, she says "can we please just talk later" and has a muslin hanging over her right shoulder, turns around, and from the reverse angle the muslin is bundled up in front of her, not over her shoulder at all. Then the angle changes again and it's back where it was before.
Power Broker - S1-E3
Factual error: Every guard in the prison has the emblems of Hamburg on his/her shoulders of the uniforms. Zemo is said to be imprisoned in Berlin, so they are wearing the wrong emblems.
Revealing mistake: The opening scene was shot twice, complete with a rear-end automobile collision in the foreground for both takes. The initial collision destroyed the taillights of the first car and the headlights of the second car and ruptured the second car's radiator on impact, spilling its contents into the street. The production crew attempted to sweep away the debris with a broom before the scene was reshot. If you examine the roadway before the two cars appear in this scene, you will see a prominent splatter on the pavement that has been swept with a broom almost precisely where the cars impact again moments later.
Continuity mistake: During the interrogation, Manolo's coat sleeve is torn at the seam. But when he leaves the room, the sleeve has no tear. (00:11:45)