Other mistake: During the garage scene, we see a large neon sign get ripped off of its mounting pole and thrown into the garage. It seems obvious that the sign is no longer connected to any sort of electricity source, however, the sign stays lit as it is ripped off its pole, into the next shot when it crashes into the garage, and then it continues to flicker a bit as it lays on the ground.
Other mistake: When Paxton and Hunt are in the shed at the end attaching themselves to the water pipe with the straps, there is an above shot looking down at them. If you look outside the window you can see corn husks barely moving on the ground despite there being an F-5 right outside.
Other mistake: In the scene in the garage pit, one of the characters is hit in the forehead by a flying hubcap. He is cut clear across his forehead, but there is only a small trickle of blood oozing from the wound. I've seen many scalp lacerations and even the most minor ones will bleed like a stuck pig, where's all of that blood?
Other mistake: When the Tree gets blown under the red truck and they get stuck on it. Why don't they ever put the truck in 4WD? You can see the front differential and 4x4 markings so the truck definately HAS 4WD. That particular year of truck doesn't even require you to get out and lock the hubs.
Other mistake: The order of action performed to activate Dorothy 2 (jumping tornado scene) and 4 (F5 tornado scene) is reversed. Also, Bill somehow has more switches to flip. Jo pressed a button, flipped a couple switches and then told Bill Dorothy was ready, while Bill had to flip the same switches, then flip some more, then press the buttons before starting to unstrap the device from the truck. (Jo didn't have to unstrap D4 because they realised at that point it had to be anchored to something heavy because the device was too light and decided to sacrifice the truck). However it is possible that Bill actually flipped the same switches twice. We can see him flip the switches, then we have a quick close shot of Dorothy 2 then the camera goes back to Bill flipping the switches again. There is no such angle change during the part where Jo activate D4, so it's very much probable that they got two angles of Bill Paxton flipping the switches, but forgot to cut one.