Continuity mistake: After Buffy finds Morgan's brain, Willow pulls up Morgan's school file on one of the library computers without even touching the keyboard. One moment the monitor is on the desktop, the next it's showing Morgan's file.
Continuity mistake: Carter and Cadet Haley enter the Stargate and we see them through the "puddle." When they come out on The Other Side, their positions are reversed.
Clash of the Megazords - S1-E29
Other mistake: When TJ goes to get the Phantom Ranger's ruby, he is standing on top of the battery pack on the Turbo Megazord. There are no other places for him to stand. After he destroys and knocks off the battery pack, in the next shot he is still standing in the same place, but there is nothing for him to stand on.
Continuity mistake: The fish that Harley uses to protect herself from the Joker changes shape and size every shot.
Hiren Lake Legend Murder Case: File 3 - S1-E6
Plot hole: The plan of the killer relies on a couple of pretty strong coincidences, such as the fact that they wouldn't realise their common link (he knows nothing about what happened on the cruise, so he couldn't know that they all wouldn't realise they have met before) and the fact that the boat is discovered at the perfect time for him to commit murder (on someone who wasn't part of the trip, but is willing to join him).
Continuity mistake: When King mentions the two brothers' "destiny", his big feline is at Young Diabolik's side, facing King and the others. Aerial shot, and the panther is at King's side facing Diabolik. (00:05:00)