Character mistake: While Hershel is sitting at the bar talking about what happened at the barn, he tells Rick what he was thinking about as he watched Rick run across the field, carrying Carl, who'd gotten shot. But it was Maggie who'd witnessed this through binoculars, and then yelled for Hershel.
Suggested correction: And he came outside to see Rick running across the field with Carl. No mistake.
Continuity mistake: Rick tells Hershel to cover Glenn. And as he's telling him to see if he can make it to his car, Hershel isn't looking at Rick, but straight ahead deeper into the bar. When the camera cuts to a different angle, suddenly Hershel is looking right at Rick. (00:13:55)
Continuity mistake: At the crossroads, after Rick starts to walk away from Shane, Shane starts to tell the story of what happened with the outbreak. Rick pauses and is looking off to his right as he is in the blurry foreground with Shane talking behind him, looking towards the left of camera. The angle cuts to a view from behind Rick, and suddenly Rick has his head turned to his left now, but also towards the left of camera but from this angle. (00:16:43)
Continuity mistake: Towards the end when Rick and Shane are leaning up against the car, Rick says it can't be that easy killing anyone, you know that. Shane is looking ahead with his head angled down in that shot, but when the camera cuts to a different angle, Shane is holding his head up right. (00:40:15)
Beside the Dying Fire - S2-E13
Continuity mistake: When the farm is overrun, the tires on Daryl's motorcycle are offroad tires. Later in the episode however, these tires change magically to smoother street tires. (00:15:35 - 00:28:40)
Beside the Dying Fire - S2-E13
Other mistake: While the farm is being overrun, Hershel is out front with his shotgun constantly firing. He never reloads and would never had the chance to stop and reload that weapon with so many zombies on him. His shotgun appears to have infinite ammo at this point.