Revealing mistake: At the end of the episode when they show Citizen Z, the computer on his left has data or some kind of code running down the screen. Right after he puts his glasses on, the pause button appears mistakenly on the screen, revealing that it's not legitimately a program running, but just a video the effects team setup.
Revealing mistake: The lady that is with the other two guys that kidnapped Murphy decides to remove her magazine from her pistol. It's an airsoft pistol. The magazine has a front feeding area for 6mm BBs, and looks weird in general. She also has no ammo, as you can see the entirety of the internal spring - not bullets. And the magazine is weird too.
Other mistake: When Doc and Wrecking Ball have to jump out of the car to escape the Z's, Doc jumps from the passenger seat, but then several seconds later, Wrecking Ball (who is driving) also jumps from the passenger seat. While it's possible he shifted over the seats, it's more likely that the crew member we now see driving the car was in the way. On top of this double-jump-out-the-same-side issue, is the fact they end up lying on the road just a few feet from each other, rather than what should be well over 100 feet apart (based on the speed of the car).
Continuity mistake: When the lieutenant and the new guy that joined up in season 2 are in the hospital, he reaches for his gun, shoots, and...click. No ammo. The lady then pulls our her gun, slide fully retracted, finger not on the trigger and states "yeah, me too." Thing is - if the slide was already retracted from running out of ammo - wouldn't she already know? I mean, she holstered the pistol. More egregiously, every shot before this, her slide was not retracted, and the pistol was ready to fire, until now, when she suddenly has a retracted slide.
Revealing mistake: During the opening credits, just before they discover the hotel, 10K fires a round from his rifle. This strikes a medallion hanging from Doc's neck and the bullet ricochets and kills a zombie. 10K ejects the spent cartridge from his bolt-action rifle. This cartridge spins in the air and lands on rocks; however, what lands is not a spent cartridge, but a live round, with bullet intact.