The Messiah on Mott Street - S2-E38
Plot hole: No one in Goldman's house finds it at all strange that a mailman arrives at the door with a letter after midnight on Christmas Eve. Nor, a short time later, does the doctor or anyone else passing by at this very odd hour wonder why the same mailman is collecting mail from a street box at dawn on Christmas Day.
Plot hole: I believe in the very first episode, during the flashback when Mick remembers rescuing Beth and killing Coraline, we see him stab her with a wooden stake, which is supposed to paralyze a vampire, as said in the "Dr. Feel Good" episode. However when Mick looks back with Beth in his arms, Coraline suddenly gets up and watches him leave while burning to "death." This is simply not possible; in the "Dr. Feel Good" episode, Mick could not release the stake himself and asked Beth to do it. This also happened in the episode when Josef was staked by the hit man that was hired to kill him, (in the episode where we meet the woman, Sarah I believe, that he accidentally put into a coma after attempting to turn her). Again, Josef was unable to remove the stake himself and Mick had to do it for him, so there is absolutely no way Coraline would be watching Mick and Beth leave; she would still be on the ground possibly burning to death.
Plot hole: The powerful 'amulet of protection' makes the bullets strike the shooters instead of John. Clearly it works not just against magic and other ethereal threats, but also against physical attacks. So why does he almost get knocked over by a car? True, he isn't seriously injured, but he was thrown to the ground. The amulet should have pulverised that car or bounced it at least two blocks away.
The Assassin - S6-E8
Plot hole: There's no way Shelley Hack could clean up all that mess of blood and three dead assassins with only an hour or so before her dinner party.
The Tale of the Mystical Mirror - S5-E3
Plot hole: It makes no sense that Ms. Valenti gives all of her employees a compact mirror and also invites them to her home. Any of them could open their mirror while standing near a painting of Ms. Valenti and they would discover the secret, as Cindy does.
Suggested correction: The compact mirror includes a palette of cosmetics. Cindy shows it to Laurel, who says, "She gave one to me, too, like we're ever gonna use it." Presumably, the employees are mostly using the free samples of cosmetics from the shop displays. I myself have owned some compacts that I didn't always want in my purse (if they were too big or awkward in a certain purse).
Plot hole: The nuclear explosion is on Liberty Island, a small yield, but nonetheless big enough to move an enormous amount of water towards the coasts on all sides. When we see Sertrakian and the others at the harbor no water is heading their way - they should be washed away by it. (00:37:30 - 00:38:45)
Plot hole: WARNING SPOILER AHEAD. The alien impersonating Skokes changed the ship's destination to Earth. This is impossible to have been done, as the first order the captain gave was to lock the course in and "Skokes" admits his security clearance was removed after his rescue from his prison. It also couldn't have been done by another alien spy, as no other survivors beyond the 4 (2 human and 2 aliens) were found and the only other alien spy was unconscious, so he couldn't have helped out in any way.
Chapter Seven: The Massacre at Hawkins Lab - S4-E7
Plot hole: The upside down should be mirrored, i.e. all left is right and right is left. When the team finds a gateway where Chrissy died, they should be seeing a mirror image through the ceiling. Also, all buildings should have been reversed. Directions to get there on the bike would have been confusing and reversed, and when any writing was seen in the upside down, it would have been backward.
The Beacon - S1-E26
Plot hole: Barrows introduces himself as "Dr. Dennis Barrows," and Teddy asks, "What's a doctor?" As the isolated villagers have never heard of doctors, Teddy would have no way to know that "Doctor" was a title/profession and not simply part of Barrows' name. He should have asked, "What kind of a name is Doctor?"
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."