Factual error: There is a periodic table shown in the background of the lab, showing an accurate periodic table as of now. During 1945, at least 21 elements had not been discovered. (00:17:40)
Continuity mistake: Rick pulls up in a car to the right side of a helicopter, gets out, and gets in the helicopter. When the helicopter is shown taking off, there is no car next to it. (00:38:20)
Continuity mistake: Near the end of the show, the squadron has to land on a carrier deck. The shots from the sky go back and forth between a straight deck carrier and an angled carrier deck. Also, an angled carrier wasn't put into use until the early 50's by the British, Black Sheep takes place in WWII.
The Whirly Dirly Conspiracy - S3-E5
Continuity mistake: When Beth glues the horse hoof on, the bottom is facing up. In the next shot it facing to the side. And then the leg changes shape in different shots.
Continuity mistake: Whenever Banner changes into Hulk his clothes rips, only his pants stays on. But when Hulk changes back to Banner, he suddenly has all his clothes on, no rips or tears at all.
Continuity mistake: Before boarding her helicopter, Jade kisses Race as her head is turned towards her right shoulder. The next shot her head is turned towards her left shoulder.
Continuity mistake: When Kimiko says "Will you two please stop abusing the English language!", Raimundo's eyes are blue.
Origin of Iron Man: Part 1 - S1-E11
Character mistake: When young Tony Stark is telling his father that their helicopter's anti-flak chip didn't kick in, he acknowledges that it was his fault by saying he blew it. When his father corrects him and says "No Tony, we blew it. Stark and Son," Tony defensively says "The anti-flak chip failed, it's not my fault," completely contradicting what he said seconds earlier. (00:14:00)
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.
Factual error: Looking at a nuclear explosion that close will burn your retinas irreparably. One can be blind 30 miles away, just by seeing the flash. The little girl at the start is looking directly at the explosion when it hits, and continues to watch.
II (The Samurai called Jack) - S1-E2
Revealing mistake: When Jack cuts the flying car's hood off, he slashes it vertically, but it is cut horizontally.
Character mistake: Tai says "And it started to snow in the middle of July" but later you find out that it takes place on August first.
Eyewitness - S1-E12
Continuity mistake: When the immortal who's trying to kill Tessa snipes at her in Duncan's car, his shot shatters the passenger-side window. When Duncan tails Tessa and her police escort to the safehouse, the passenger-side window is intact. (00:30:05 - 00:35:50)
Revealing mistake: When Shalimar is getting ready to leap on Gabriel, there is a quick glimpse of support wires attached to her.
Forever Red - S1-E34
Plot hole: Tommy states that he and the other Zeo Rangers destroyed the Machine Empire's leaders and ultimately destroyed the Machine Empire except for the Generals who escaped. This is not true - Lord Zedd and Rita destroyed the Machine Empire leaders at the end of series 4, and the Space Rangers destroyed them again in Countdown to Destruction in series 6. The Zeo Rangers never destroyed the Machine Empire.
Suggested correction: How would Tommy know that? He didn't watch the show or know the ins and outs of what happened in space. This is what he believed based on his experiences on Earth. Everything you described is factually correct, but Tommy did not witness this. So, to his knowledge, he destroyed the Machine Empire.
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.]
Revealing mistake: When Pablo as the ping pong bandit takes Tyrone's paddle, Tyrone asks if he can play Pablo again so can get his paddle back. When Pablo walks into the frame, his skin clips out of his coat. This also happens when he does the "Bandit Slammit".
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)
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.