Vampire Bats and Scaredy Cats - S2-E2
Continuity mistake: When Lisa's uncle shows her her grand-father's picture, it changes from one shot to another.
Hang in There, Scooby-Doo - S2-E3
Continuity mistake: In the cavern, Scooby and Shaggy dig holes in the ground. The rest of the group notice a truck drived by the Pterodactyl going toward them. Discs and cassetes fall from it. The shot later, the stones behind them have disappeared and the pile of discs have a different shape.
Revealing mistake: During the opening credits, after Merlin appears, we see Shaggy for about 1-2 seconds with no arms.
Continuity mistake: In the episode of Scooby movies where they meet the Three Stooges, Fred says that Velma is missing and they need to find her. When they go off to look for her they pass a window. Fred first, Daphne, then Velma (despite her being the one missing!), Shaggy, then Scooby.
Vampire Bats and Scaredy Cats - S2-E2
Other mistake: When the Mystery Company find a torn paper in a coffin, it is written exo-6 and something else. They find later that exo is the first part of exotic. The way the paper was torn, you should be able to see the lower part of the missing letters.
The Chiller Diller Movie Theater - S2-E4
Continuity mistake: Scooby Dum's collar goes from its usual red to yellow briefly in one shot on the train.
Scooby's Chinese Fortune Kooky Caper - S3-E12
Continuity mistake: When Shaggy and Scooby start changing the Mystery Machine's back right tire, it's flat. When the Moon Monster shows up it's fixed, and they've just started jacking it up.
The Harum-Scarum Sanitarium - S1-E11
Continuity mistake: Fred and Velma get chased by one of the dogs into the room where Shaggy and Scooby are. Daphne wasn't with either pair, yet she's suddenly there once Fred closes the door.
Factual error: There's an exhibit in the Smithsonian Institute that shows Benedict Arnold, William Demont, and Major John Andre labeled as Famous American Traitors. One problem, Andre wasn't a traitor to America as he was a British officer to whom Benedict Arnold arranged to surrender West Point to during the war.
The Chiller Diller Movie Theater - S2-E4
Plot hole: Given Jim Moss, the studio chief, is already on the train, it makes no sense for him to have been in the coffin. That and how he managed to slip into it without being seen by the conductor or anyone else.
The Creepy Creature of Vulture's Claw - S3-E10
Other mistake: The whole time Professor Greer's the Mantis he's around seven feet tall. When he's unmasked he's suddenly his own size again.
The Creepy Creature of Vulture's Claw - S3-E10
Deliberate mistake: Professor Greer's fleeing from the room one moment, then suddenly he's behind the gang dressed up as the Mantis.
The Creepy Creature of Vulture's Claw - S3-E10
Plot hole: It's not explained how Professor Greer, a man of medium height, say five feet seven inches tall, could make himself look like he's seven feet. Maybe stilts but those would surely protrude out.
The Ozark Witch Switch - S2-E6
Plot hole: It's never explained how any of the Hatfields could've left a pile of sawdust at their cabin.
Plot hole: Given it's a government building there's no way the ghosts could drill into the U. S. Mint and not draw security's attention.
There's A Demon Shark In The Froggy Dark - S1-E9
Deliberate mistake: Unless they're super strong, none of Mystery Inc could've thrown an anchor to the top of a cliff.