Factual error: When they are at Aunt Meg's the first time, they get word that a tornado has been spotted and somehow they already know its rating. Tornadoes get their ratings from the amount of damage they do. This is determined after the tornado is gone.
Other mistake: When the twister hits the drive in theater, the sirens are wailing, but nobody reacts. Only when Jo screams at the waitresses they start panicking and run. The movie is set in Oklahoma, smack in the middle of tornado alley. The people there know what the sirens mean, they sure don't need no out-of-town big-shots to tell them to get under cover.
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.
Stupidity: In the opening, it's surprising that Jo and her family have to actually go outside and run even a short distance to get to their cellar. Farm houses, especially in tornado prone areas like rural Oklahoma, would typically be built overtop of the cellar, which would be accessible from inside the house. Furthermore, Jo's cellar door seems to be secured with what seems to be little more than a latch much like those used for restroom stalls! Not very practical for a door intended to protect the interior from outdoor elements.
Continuity mistake: After the first tornado when Jo's truck is destroyed, you see Bill's truck with a shell on it. When their group is leaving the scene, the shell is gone and one of the Dorothys is in the bed. Where did the shell go?
Plot hole: During the scene when Jo introduced the first Dorothy to Bill for the first time, you can see the blurry figure of Dusty and Dr Melissa holding hands in the background, which is super weird given she was annoyed by his presence at that point.