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.
Plot hole: In the Pudding Club episode, when they visit the secret room, all the candles are lit even though no-one is in there.
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.