Factual error: When Rick has given Andrea his revolver to end her life, he leaves the room with the others to leave Andrea and Michonne alone. The next thing you see is Rick, Tyrese and Daryl waiting outside the room. You hear the gun go off and then you hear a tinkle as a shell casing hits the floor (noticeably "lighter" than the sound the revolver would make when dropped). Revolvers do not eject a shell casing.
Continuity mistake: In the scene where Merle is the in big box late 80's chevy with big 20-22 inch rims he is shown driving it in the barn yard drinking, playing music, and zombies following him. The shot changes a few times within the same scene with the big rims on, in one shot the car is shown with him driving it but the stock rims (15") are on the car, the paint of the car looks a little darker too. Then the shot changes again while he is still driving it and the big rims are on the chevy again. The shot that shows the stock rims is a pretty fast shot so it could be easy to miss.
Continuity mistake: At the start of the episode when Tyreese and Carol are walking down the railroad tracks towards Terminus, they encounter a herd of walkers coming out of the woods. One of the first walkers to cross the tracks is a male walker wearing a burgundy sweatshirt with a rip in the middle. When gunfire erupts at Terminus, the walkers turn their attention towards it. In the next shot when they start to head towards the sound, we see the same male walker now in the middle of the herd yet to cross the tracks, next shot after that, we again see him at the front of the pack.
Visible crew/equipment: During the scene where Daryl's group finds the auto shop, Daryl spits on his hand to wipe the window and is surprised by a zombie banging up against the window. He says, "Got some friends inside" and walks away. The camera pans to the window and a crew member wearing a white hat and (what appears to be) an orange shirt is visible in the reflection. He seems to be taking a picture (probably for continuity, which is pretty ironic).
Continuity mistake: Glenn demands that Abraham stop the truck so he and Tara can get off, the two male characters then have a scuffle. We can see Eugene in the background standing next to the truck facing right of the camera. But when the camera cuts back to Eugene by himself, he's now facing the opposite direction. Also the items in the back of the truck move from left to right.
Continuity mistake: When the Winnebago breaks down. Shane and T-Dog offer to drive ahead to check out what could possibly be a gas station. Shane tells Rick to hold the fort while they're gone. Meanwhile Rick is dealing with dying Jim. When discussing Jim's predicament, Shane is there, he hasn't gone anywhere. Then when they put Jim under the tree T-Dog is there too. Then they all drive off like the breakdown never happened. Nothing is mentioned about whether Shane and T-Dog found a gas station and if they did, it was very quickly sorted out - two minutes tops.
Other mistake: When Nicholas shoots himself, both him and Glenn fall with their feet facing the dumpster, and their heads facing the walkers. However, when they cut to the shot of presumably Nicholas being eaten, we see Glenn's head facing the dumpster. This does not make any sense. Glenn would have had to do a complete 180 turn before landing, or move around without being detected by walkers. In fact, the way they landed does not make complete sense at all. Another possible explanation could be that there are two dumpsters, but none is seen. The fence seen when Glenn and Nicholas climb on top has also disappeared.
Continuity mistake: As the group kills the walkers that come out of the barn, the camera shows several different vantage points from in front of the barn, inside of the barn etc., it shows the walkers lying with a clear path between them, and in another it shows the walkers lying in a jumbled pile with no path between them. This goes back and forth a few times until Sophia comes out of the barn, and there is no clear path again.