There are a few times when Jack and Claire are talking and looking at each other, and they can't see Charlotte, but Charlotte doesn't disappear. However, the director has said in an interview that the rule is you *won't* disappear if someone is watching you, not that you *will* disappear if someone isn't.
While Jack and his girlfriend are in bed, the camera comes down beside Jack and the girl's head is barely visible on the other side of him, but it can be seen to slide down as the actress gets off the bad. At that point, the character hasn't actually vanished like the others because she says one more short line of dialog.
When Jack answers the phone it is clearly unplugged. You can clearly see the port for the cord on the bottom which cordless phones do not have.
During the car journey to the resort, it is told that there is only one road in, and then nothing else for miles. Yet when they pull into the resort, the sign says it's the last place to rest for 300 miles. This means there is at least one other road exiting the resort, so there is more than one road in.
At approximately 16:10 into the movie, shortly after Alex says he's not moving the car away from the pump until he gets gas, a couple people can be seen walking through the woods behind Claire's right shoulder. They could be either crew or some hikers that got caught in the shot.
After Alex is shot through the shoulder, bandages are put on him over his two t-shirts, instead of having the shirts removed to bandage the wound.