Continuity mistake: When Buffy is talking to Riley, she puts the scarf on her head, on his hand. He talks to her and says "Maybe I am the bad guy," and in the next frame her scarf is back on her head again, then off again in the next frame. (00:24:20)
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.
Super Nova - S1-E2
Revealing mistake: When Stan, Xev and Kai are walking to the Memory Chamber, they seem to walk out of a two dimensional line at the lower left into the scene. The set and green screen weren't quite synched.
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.