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 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 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. If the room is hot enough to warp stainless steel doors, wouldn't these ice blocks have been vaporized long before?
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.
For several of the fireballs Charlie shoots at the mansion, the guide wires are clearly visible. Furthermore, the explosion from one of the fireballs hitting the mansion, goes of before it reaches the window.
During the final scene at the farm, Charlie sends columns of fire along the ground at the government men. You can see the blue edges to the flames, indicating an accelerant was used to produce the fires.
When the spigot goes flying across the barn, it hits the wall next to a stall belonging to a horse named Champ. The shot is reversed, the name and letters on the stall door are backward, as if the scene was shot through a mirror.
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.