The Secret of the Unicorn: Part 1 - S1-E3
Deliberate mistake: After Francis Haddock kills Red Rackham, he lights a fuse to the explosives. The fuse that was lit is only a foot long, yet he is somehow able to climb out the ship without anyone noticing, get into a boat and swim all the way to land before it explodes. At a foot long it would have exploded in 10 - 15 seconds, all of that would taken at least 10 minutes. (00:18:45)
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.
Deliberate mistake: During the episode, whenever daily newspapers are shown, they lack any indication of the date.
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.
Deliberate mistake: We see the Air Force plane's bomb bay doors come open. But in the next shot of the plane banking, the doors are instantly closed again. (00:45:20)
Deliberate mistake: When Jaime sneaks out of the window, a bright cinematic spotlight is cast around the window, contrasting with the dark night of the following wide shot.
The High Life / Best Friends - S2-E10
Deliberate mistake: In "The High Life", there is a scene where Stinky submerges his head in a tank of water. He delivers the line, "Gee willickers, it's still ticking", and everyone somehow understands what he is saying with his head underwater.
Suggested correction: Nobody responds to what Stinky says, so there's no reason to assume that everyone understood him.
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)
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: To fix the error of the Enterprise firing phasers from the torpedo bay, the Blu-ray version uses footage from "The Best of Both Worlds" to show phasers firing from the dorsal emitter. In doing so, they created a new goof; the planet El Adrel is not visible in the background during these shots.
Suggested correction: I rewatched the original version on the old DVDs. El Adrel wasn't visible in the original either, so this is not a new error.