Luna's shoes change from high heels to flats when she crosses the lake on Miles' back (in the "raft" costume).
When Miles is stuck in a tree, he is wearing blue jeans, but both before and after that, his pants are black.
In the final chase scene, the all-white futuristic vehicle is replaced briefly by another all-white futuristic vehicle of a different design, including a black trim.
During her party, Luna suggests that everybody go for a swim. But when she and Miles are running from the police she claims she cannot swim.
When Miles is first awoken from the cryogenic freezing process he has tin foil under his suit. During the process of sitting up, the foil mysteriously disappears from around his neck/chest area.
The Volkswagen could not possibly start after 200 years in a cave. Gasoline typically has a 30 day shelf life. After 30 days the aromatic parts of the gasoline noticeably start to evaporate, and it begins a chemical breakdown process into gum, resin and varnish which cause misfires and poor starts, poor performance, and could cause engine damage. Degraded fuel in a running engine also leaves deposits in the carburetor plugging essential passages and can also leave deposits on the intake valve stem causing it to hang up and not close properly or even not to close at all.
The Woody Allen character, under hypnosis, states that his first wife wanted a divorce in 1963 because he "drank his waterbed." This could have never happened. Waterbeds had not been patented until 1971.
The Volkswagen's battery would have long since died.
The rubber tires on the Volkswagen could not have survived 200 years in the open air.
The attempts to losen the lug nut make less and less sense. Accelerated corrosion would still not be nearly fast enough to make any difference and odds are it would make the problem worse. And if there was enough thermite to remove the nut, it would remove the stud right along with it. Also odds are it would weld the rim to the hub for good instead of losening the lug nut.
When Luna swings across a creek the action is performed by a male stunt double in a wig and the character's outfit.
The tow cable for the raft costume is visible.
When Miles is trying to escape with the flying device (the one that mounts in the back) the tow cables are visible in one shot
Not everybody gets the joke about the VW starting up after 200 years.
While Miles is describing the artifacts from the 1970s.
The "AIRES" project is apparently misspelled on the visible screens during the scientific briefing. If, in fact, it refers to the astrological sign or constellation, it would be spelled "Aries." If it refers to the god of war, it should be spelled "Ares."