When Rick returns to the prison from his search he gets out of the car to talk to Maggie and leaves the door open. In the next shot the door is closed while Rick is talking to Maggie. When Rick walks back to car the door is open. Rick does close the door when he exits the car. However the door alternates between open or closed several times in this scene.
As the fences are collapsing, Rick and Carl are shooting at the walkers to stop them. Both are shooting, holding their guns level. Rick even kneels down at one point, still shooting level. As they'd have to take head shots to stop the walkers, and at their close range, they'd need to be aiming upward, at the heads of the walkers, to stop them.
When Herschel and Maggie are trying to save Glenn (~33:40), Herschel (who is supposed to be an amputee) runs up to them (without crutches), then kicks his right foot up behind him while standing on his left leg. However, according to The Talking Dead Herschel has a prosthetic brought back from a previous run.
It took months of walkers leaning on and pushing against the outer fence for it to collapse and give in, yet when the walkers get through the outer fence they are somehow able to push down the inner fence in a matter of a few minutes. And the spot they push down is where the fence attaches to the guard tower, which would be the strongest part of the fence, unlike the middle which is where the outer fence gave way.
Rick runs to quickly open the gate as soon as he sees an unknown van approaching. It ends up being the van Daryl's group procured after losing their Charger, but he couldn't have known that from that far away. After being attacked multiple times by the Governor, Rick should have been very wary of a vehicle that he didn't know speeding up to the gate.