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.
Young Kidaichi's Murder: File 1 - S2-E1
Continuity mistake: When Takanori the cameraman says "He's dead", everyone in the reaction shot is much closer together (and to Itsuki) than in the earlier angle. (00:14:45)
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)
Plot hole: During Ryder's report, as Bruce and company watch it on TV, the camera suddenly zooms in on Joker standing on a catwalk above Ryder, and none of the crew, especially not the camera man who caught the villain, makes a comment about this. They may have thought the Joker (or rather an impersonator) was perhaps a surprise gag in the show, but since this is supposed to be a serious documentary report, it is still strange that they wouldn't point it out.