The Sinner and the Sandman - S5-E2
Plot hole: Ian Avery-Cooper loses his lottery ticket which is immediately picked up and appropriated by Leonard Corbyn. However, Avery-Cooper immediately reports the loss to the shopkeeper who sold him the ticket. All lottery sales staff are trained in what to do under these circumstances, because it happens a lot - they cancel the lost ticket and issue a new one. Since Avery-Cooper used the same numbers every week this would not pose a problem, but even if he didn't the ticket would be recorded on the seller's computers and could be precisely reconstructed. This would be even easier since Avery-Cooper reports the loss within a minute of it happening and we see that he has the receipt for the sale in his hand. Corbyn's stolen ticket would be worthless and Avery-Cooper would be able to claim his rightful winnings. If nothing else Ian could have simply bought another ticket with the same numbers.
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.
Plot hole: Throughout the show it is reported several times that Billy and Ally met when they were both eight years old in a park by sniffing each other's bottoms. However, when Billy is buried in season 3 his tombstone reads, 1968-2000, making him 32 years old. Ally is only 29 and does not turn 30 until later in that season which would at the very least, put them 2 years apart. (00:41:15)
Continuity mistake: In the first episode of season 10, when Marissa is holding a dog while talking to Elaine, the way her arm lies around the dog's neck changes several times between shots.
Visible crew/equipment: When T.J. is playing basketball in the garage, before the helicopter scene, you can see the boom mic fly across the top of the screen for about 2 seconds.
Continuity mistake: When Sheila Carlisle has hanged the dead head up on the wall of Eugene's office, they are all looking at it and the eyes are looking straight in to the room. Later in the episode, the eyes are looking more to the right.
Academy's Seven Mysteries Murder Case: File 1 - S1-E1
Continuity mistake: During the introduction of Sakuragi's card puzzle, the cards change position between shots; for instance the two of spades in close-up bridges across two adjoined desks, while it's in a completely different spot in other shots. (00:07:40)
Continuity mistake: When we first see Darren's sister coming out of the apartment she has a pram with her, but there's no baby in it, but in the next shot were we see her go back inside and up the stairs she is carrying her baby.
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.