Plot hole: Gary is still "alive" because his head/brain was not destroyed when Shiela killed him. However, over the course of the show, we see many bodies in the freezer or otherwise with the heads still intact yet none of them are still "alive" in spite of the fact that their brains have not been dispatched.
Other mistake: When Sheila was eating Gary she bit and chewed his entire finger only then to later find that Dan had found that exact same finger in their yard.
So Then a Bat or A Monkey - S1-E1
Revealing mistake: When Joel puts the dead body in the freezer, the eyes are open. When he pushes the head to the side so he can close the lid the body plainly closes his eyes.
So Then a Bat or A Monkey - S1-E1
Continuity mistake: In the beginning when Joel wakes up, he looks at the clock and it's 6:58. He wakes up Sheila and they start talking. Less than 45 seconds pass and the alarm goes off at 7:00.
Continuity mistake: When Sarah takes Eric's taquito, she takes with her right-hand and switches it to her left. In the next shot it's back in her right hand.
Continuity mistake: When Sarah grabs a taquito, she uses her left hand, then switches it to her right hand to bite it. In the next shot it's back in her left hand.
Continuity mistake: When Sara takes a taquito, she grabs it with her left hand, then puts it in her right hand and starts to eat it. But in the next shot, the taquito is back in her left hand.
The Farting Sex Tourist - S1-E4
Continuity mistake: Joel takes a grilled cheese to Abby in her room. He takes a bite, hands the sandwich to her, and she takes a bite. In the next cut, the sandwich is sitting on the plate, untouched.
Strange or Just Inconsiderate? - S1-E7
Continuity mistake: When Abby finds the hidden door in the garage, she and Eric pull away the shelf to see what's behind it. By moving the shelf the door opens approx 45°. In the next shot the door is closed again and Eric has to open it by hand. (00:09:25)
Wuffenloaf - S3-E1
Plot hole: When Abby and Eric return the night vision goggles, Abby asks if they should put them back exactly where they were and Eric says he didn't remember where they went but luckily he "took a picture" of how it looked before. How could this be possible if Abby purposely excluded him when she collected those goggles from Lisa?
Wuffenloaf - S3-E1
Continuity mistake: When Joel takes the note off the door, the knife slices the paper. But in the next shot, where they're facing the camera, the note has a chunk ripped out on top.
Knighttime - S3-E2
Other mistake: When Abby uses her phone to show Eric the pictures that Sven posted on Instagram, her phone states it is 11:26pm when you can see it is daylight after they walk back into Eric's room straight after. (00:05:00)
We Let People Die Every Day - S3-E3
Continuity mistake: Joel gets himself a potato with some toppings. In the first shots you still can see the potato underneath the toppings. Right before Joel starts eating his plate is much more loaded and the potato is drowned by so much topping that you can't see the potato any more. (00:08:50 - 00:09:14)
Continuity mistake: The organ Jean is holding while talking keeps changing shape without her eating it. Sometimes the edge is jagged, has a bite out of it, or is smooth. And we usually see her holding it, and she's not twisting it around.