When he first visits Charlie in quarantine, Captain Hollister removes his code-key badge twice as he prepares to leave the room.
It is mentioned several times that Andy cannot use his mind-control powers without placing his hands on his head. But when he blinds the Shop men, he uses his powers while holding Charlie.
In the scenes where Rainbird plays "John, the friendly orderly" the eye-patch he wears as part of his disguise is in some "John" scenes, but not others. Also, sometimes he wears the patch over his left eye (during the blackout) and sometimes it's over his right eye (when he and Charlie are with the horses).
When Cap Hollister is first in the room with Charlie, the door behind him is open over his left shoulder after he had closed it. Then when the camera shot changes again the door is closed.
When Andy is walking with Captain Hollister and is about to 'push' him, you can see a dark bloody line under Andy's nose. But this only occurs after he 'pushes' someone. This would appear to indicate the scene was shot repeatedly.
In the barn scene, the water spigot turns clockwise, then detaches from the water pipe. It should have turned anti-clockwise.
In the scene where Charlie's abilities are being tested in the lab, she completely incinerates a cinder brick wall. Yet, the ice blocks do not boil until after she turns her attention to them. Since the room is hot enough to warp stainless steel doors, these ice blocks would have been melted long before.
Soldier in airport shows he is with the special forces, green beret's. He has private first class rank when he should be a sergeant or higher for that specialized force.
In Charlie's first test, the technician has to use a card key to run out of the room. You see him use it and hear the doors rumble open. A second later, the focus is on Charlie, and we can hear the rumble of the doors closing. Yet, as Rainbird points out, Charlie walks out the doors which have somehow re-opened without the need for a key.
When Charlie is destroying The Shop's mansion you can clearly see where the set was cut so it could destroyed easily. Right after Charlie sends the second fire ball into the house the shot pans up to the balcony where a man is burning. In that shot you can see where the balcony has been set to be destroyed. You can also see the detcord explosives wrapped around the pillars to cause them to break off at predetermined places.
When Charlie is destroying The Shop's mansion you can clearly see where the set was cut so it could destroyed easily. Right after Charlie sends the second fire ball into the house the shot pans up to the balcony where a man is burning. In that shot you can see where the balcony has been set to be destroyed. You can also see the explosives wrapped around the pillars to cause them to break off at predetermined places.
Obvious stunt double for Charlie when jumping off the overpass into her father's arms.
When Charlie's dad gets shot with the dart in the wide shot from the viewfinder of the rifle, he reacts to the shot but he has been hit with nothing, then in the next, closer shot the dart just appears.
When she sets the barn on fire you can clearly see a shiny "coating" that has been painted on the horse stalls to "control" the way the stall flames up.
In the end credits "Special Effects" is misspelled as "Speical Effects".
When Andy grabs Charlie and runs (right after she sets fire to the airport security guard) she yells, "I didn't mean it, Daddy!" but her mouth never moves.
When Charlie throws the three agents in silver fire suits out of the barn after setting them on fire, the wires used to pull them back are clearly visible as the barn door breaks.