Deliberate mistake: After the trilithium missile hits the sun, it is shown going out in real time from Veridian III. As the planet is relatively earth-like, it is several light-minutes away from the sun. The filmmakers wanted it to be obvious that the missile was successful, so they ignored the speed of light. (01:20:35)
Deliberate mistake: When the recon team head out of the base they encounter a robot. But it is a probe droid, distinguishable by the lack of a cannon on its right arm. The only probe droid that the lab sent out self-destructed back in the 1970s, the rest were all sterilisation units. (00:39:05)
Deliberate mistake: Vega's claw never actually hits any of the furnace buttons, but it opens up anyway.
Suggested correction: The claw penetrates the panel cover and most likely shorted the wires inside. You don't have to actually press any buttons to activate it if you short the wires.
Deliberate mistake: While Jimmy and Billy are being chased by the jet skis one of the baddies fires a missile, and when it lands in the water the long shot is flipped, note "AKZO" is backwards. (00:49:25)
Deliberate mistake: During the final battle, at one point Sean kicks Crane off a rope bridge. When this happens, if you look closely you can see the rope railing on the side of the bridge fall away right before Crane falls. It's supposed to look like Crane is falling through the ropes, but they drop just a split-second too early (he's not even touching them when they start to fall), so it was done on purpose and mistimed. (It was likely timed to drop away just a split-second before Crane fell so that the stunt-person wouldn't accidentally get tangled in the ropes as they fell).