Revealing mistake: When the Governor is hunting Andrea, he smashes a few windows in the building where she's hiding. When he breaks the first two, there's a jet of steam or air, showing that it was broken a split second before he hit it with the shovel. (00:29:04)
Other mistake: In Woodbury, on the street, while Andrea talks to the Governor, we can see everybody wearing jackets and orange, red and yellow trees, showing that the scene was shot during fall. According to the beginning of the third season, they had just passed through a hard winter. So it should be spring or the beginning of summer.
Revealing mistake: After Andrea avoids the truck on the road, she is attacked in the woods by some walkers and pinned to a tree. After breaking free, she goes to stab a woman on the ground with her knife. But as she goes to strike, you can see the actress slowing her strike down "pulling the punch" and gently resting the blade on the walker's head instead of actually striking. (00:20:41)
Answer: The walkers could have knocked them down more than once. There may have been another wave that knocked down the fence earlier and they're going to put it up again soon.
Captain Defenestrator