Continuity mistake: When Josh has got out and they go looking for him, they find Aiden on a small bridge. From a distance he's got a very dark sweat stain on his shirt. In a closer shot it's faded to nearly nothing, and gets lighter/darker in different shots throughout the scene.
Visible crew/equipment: When Adrian is getting something from the snack machine, the cameraman can be seen in the snack machine's reflection. (00:26:30)
Visible crew/equipment: When Michael Fay (1st Vampire ground zero) enters the cabin to escape the police, the film crew can be seen through the porch railing at the bottom right of the screen. (00:40:53 - 00:49:47)
Continuity mistake: When we see Coraline in Mick's vision of when he was taking her dress off at a party, her tattoo is under one of her shoulders (I think it was her left one) but later on in the series we see Morgan/Coraline wipe off the make-up on where her tattoo is...on the opposite side.
Continuity mistake: When Marshall first finds Trip's letter, he holds it from the left side. In the close-up, he's holding it from the right side. (00:02:10)
Revealing mistake: As Sgt. Cain and Chief Lain stand by Marjorie's dead body lying on the hotel bed, discussing her death from an overdose, you can see her stomach rise and fall slightly, though she's supposed to be dead. (00:18:00 - 00:20:00)
The Gloaming - S1-E6
Continuity mistake: When we first see the guy in the tunnel, he runs to the left in the first shot. The next time we see him, he runs to the right.
Factual error: Constantine's driving licence is shown - it's a UK licence, but no. 7 where his signature should be is blank, and no. 8 where his full address should be simply says "England, United Kingdom." Both are printed onto the licence when it's issued - without that info it would never be issued in the first place. And it's not a fake, because why would he have a fake licence with his real information on it? It's just an incomplete prop.
Continuity mistake: "The Feverman": Before putting the chain around his neck, the doctor removes both his detachable collar and his black string tie. A few shots later, not only is the collar back, but he's now wearing a red ascot-style tie. Both collar and tie vanish again one shot later. (00:17:05)
Royal Jelly - S2-E1
Plot hole: It's all very well for Albert to humm "bzz-bzz" to indicate that he has been eating too much Royal Jelly and is no longer entirely human. But "bzz" is just the noise of bees flying, it's not a sound that they deliberately produce. It makes no sense to SAY "bzz." Suppose he was turning into a horse instead, then he might say "Whinny!", but he wouldn't say "Clip clop clip clop."
Deliberate mistake: Identical twins Beverly and Elliot have the exact same beauty mark on their faces, roughly on the smile line directly across from the right nostril. Identical twins don't share features like that.