Visible crew/equipment: In the scene where Billy and Jo go into Jo's aunt's house to rescue her after a tornado has gone through Wakita, they hear things falling. When they jump over a break in the floor, if you look closely, there is a crewman in a white shirt that runs across the gap.
Continuity mistake: When Bill and Melissa go out to get the divorce papers from Jo, we see Bill pull his truck up with Rabbit and Allan's truck (hood up) in the background. We see it closer up when Bill asks Dusty, "Where's Jo?" But when the scene comes back to Bill and Dusty and then shows Melissa, Rabbit, Allan and the truck have disappeared. When Dusty is holding Melissa's hand and walking to sit in his chairs, Rabbit & co. are in the background again.
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.
Suggested correction: Sirens go off so many times that true Okies tend to ignore them. We might get nervous if the cable goes out.
Do true Okies also run screaming the second an out-of-town big-shot yells at them? Sorry but that argument just doesn't compute. People ignoring fair warning simply isn't a thing in the movie. The main plotline is people not getting warnings soon enough.
It's also possible that they did hear the siren, but unlike the people at the drive-in who could actually see the tornado tearing the screen apart, the people at the snack bar might not have been able to see it (especially with an awning over the windows). They were probably at most confused as to what was happening and it wasn't until Jo actually said to get underground that they realised it was real and was actually happening.
Continuity mistake: When the telephone pole falls on the bed of Paxton's truck, the pole dents the bed. In the scene before the pole falls, there is a dent on the bed.
Other mistake: When Bill and Jo are strapped to the water pipes in the final twister scene, after the tornado passes and they are back on the ground, one of their leather straps are already broken. In this condition it never would have held itself on that pipe, let alone an average sized human being.
Factual error: With the last Dorothy, Bill and Jo burst open the door of the Dodge and make a run into the cornfield. This is not possible. Corn stalks are strong and would hold the doors back, no matter how hard they pushed. Bill Paxton and Helen Hunt were unable to open the doors during the scene, so it required them to open the doors before they entered the cornfield in order to jump. They filmed the scene of them driving through the cornfield and start opening the doors. Then they cut and restarted filming, this time with the doors already open so they can jump. Then careful editing was used to merge the scenes together to make it look like one.
Visible crew/equipment: When Jo is introduced to Melissa, Melissa says, "It probably seems kinda sudden." Look into her sunglasses when she says this; you can see a rectangular shaped figure. Figure of the camera, possibly?
Factual error: When the team is attempting to intercept the second tornado, Bill floors the gas pedal in the Dodge Ram after Jo expresses disgust at how slow he's driving. The next shot shows the dashboard, where the speedometer moves from 50-70 MPH, the engine is heard accelerating in the background, but the tachometer stays around 1500 RPM. The truck is an automatic and so it would have downshifted when Bill pressed the accelerator to the floor, and therefore revved much higher.
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.
Suggested correction: Character mistake more than anything. In a panic situation you don't tend to think of the obvious solution. The other issue to is that even if the truck was in 4wd that it might not have been enough. Keep in mind that the rear tires did burnout on a few attempts so the issue wasn't that the wheels weren't stable on the ground but that the tree trunk might have been too big to get the wheels over it by driving across (especially from the angle they were at).
Factual error: If an F-5 has enough suction to pick up a full gas tanker, why did it not pick up Bill's red pickup at the same time? It definitely had enough power to lift the tanker again, so it should've taken the pickup too as the tanker passed over it.
Other mistake: When Jo readies Dorothy IV on the back of the truck, she switches it on, but she never releases the rubber catches holding the lid in place.
Suggested correction: The rubber catches weren't needed to open the machine; they were only there to secure the entire lid in place. As seen when Jo is first showing how Dorothy works, the lid could be opened manually or automatically, depending on which button you pressed. As long as the pack was "set up" (sirens on and buttons activated), the pack would open automatically when close enough to the tornado, as shown when the pack lid opens at the end.
The way I understood it, the rubber catches were there to secure the lid in place during travel and had to be released for the automatic opening mechanism - the existence of which you are entirely correct about - to open the lid. That makes sense entirely, if you are bouncing over rough terrain, you would not want to load gears or servos with the considerable force spikes thick acrylic panels would impart on them were they not otherwise secured.
Continuity mistake: As Bill and Jo pass the camera position, the red lights on Dorothy are flashing. A moment later, Bill actives Dorothy, including the lights.
Revealing mistake: When Bill and Jo are driving towards the first tornado together (arguing), it's clear there's no windshield in the red truck. There's no rear view mirror and it's perfectly clear. During the next few scenes, a rear view mirror appears and there is mud on the windshield around the wiper tracks.
Visible crew/equipment: When Bill's fiance is driving over after the first tornado, when the truck lands, she swerves and she stops. As she is getting out, a camera is visible. When the camera backs up though, a crew-member pulling it back is visible in the door.
Continuity mistake: At the beginning of the drive-in scene Jo and Bill give each other a long look. During this you can see that Jo passes the same Pepsi sign twice.
Continuity mistake: When Bill & Jo leave the aunt's house in the red truck, it shows the truck has a back sliding window - the next shot there is no back sliding window.
Factual error: In the first sequence, the family is in the house with the child in bed. It looks to be night. When they run from the house to the shelter, they scatter a flock of chickens. Chickens don't go outside after dark, even during eclipses and such.
Continuity mistake: When Bill is walking over to see Jo for the first time, he passes Joey working on the hood of a truck that was previously shown in front of the blue Doppler van and next to the green tractor. Throughout this sequence, this taupe/brown pickup with camper flops back and forth between the two places. Lawrence finally drives it off.
Revealing mistake: The weather really is unusual in Oklahoma, as in some scenes, the cornfields were ripe and brown, and in others, they were fresh and green. Obviously shot at different parts of the season.
Continuity mistake: In the first few seconds of the movie, there's a landscape shot of a fence. Right in front of the fence there's a little piece of grass blowing in the wind, and it's just so obvious that they looped the 1 second to make it last 5 seconds, because the grass keeps jumping back and forth. Minor but annoying.