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.
Revealing mistake: During the opening credits, after Merlin appears, we see Shaggy for about 1-2 seconds with no arms.
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.
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 Ghost of The Bad Humor Man - S1-E4
Continuity mistake: The back doors of the armored truck that the phantoms are trapped in go from being open to closed to open again.
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.
Scared a Lot in Camelot - S1-E10
Other mistake: Fred calls out to the Black Knight ghost who sees and hears him. Yet it's Shaggy and Scooby in different armor who enter the room.
The Harum-Scarum Sanitarium - S1-E11
Continuity mistake: Shaggy goes back and forth from being in the front seat to the back seat of the Mystery Machine as the episode starts.
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.
A Frightened Hound Meets Demons Underground - S1-E14
Character mistake: Velma mentions Seattle burned down in 1890. The fire went from June 6-June 7 1889.
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.
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.
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 driven by the Pterodactyl going toward them. Discs and cassettes fall from it. The shot later, the stones behind them have disappeared and the pile of discs have a different shape.
Hang in There, Scooby-Doo - S2-E3
Continuity mistake: The pile of bootleg records suddenly gets bigger after Velma's shown holding some of them.
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 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.
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.