Jonnie Goodboy Tyler's hair constantly changes length throughout the film.
When Jonnie gets off his horse, he hands Chrissie the medicine. However, after Chrissie tells him that his father has died, he throws the medicine in despair.
When the Psychlo Dome finally breaks, massive sheets of glass and girders can be seen falling onto the buildings below in wide shots. In closer shots with actors, small chunks of glass can be seen falling, without a girder to be seen. Also, whole buildings collapse, and yet we see just dust and small chunks of rock hit the ground.
The heroes find fully fueled and armed 1000-year-old Harriers (actually AV-8Bs) on the pad at Fort Hood, Texas. Fort Hood is a US Army installation. The only US service to fly the AV-8B is the Marine Corps.
We see the nuclear weapon used to destroy the planet Psychlo pulled out of a cruise missile. A warhead cannot be yanked out of the missile and detonated without the fissionable material being removed and built into an entirely new device. This a safeguard to keep them from being pulled out and used in exactly this way.
When Jonnie Goodboy Tyler is thrown out the aliens pull his mask and bet how long before his lungs explode as he runs seeking help he passes several open fires. How could they burn without oxygen?
Evidently during the movie the Special FX crew couldn't decide how many fingers the Psychlos have. Depending on the Psychlo character, some of them have hands with five fingers and some with six, though it's argued that one hand has five and the other six. However, Terl's right hand changes between six and five fingers several times between scenes.
When we first see the ruins of Denver, there is a bright red car in the foreground. Then, we see the rusted hulks of other cars. This red car would have had a phenomenal wax job to stay shiny outdoors for a millennium.
Many of the human males apparently were able to shave everyday or so, since few had beards.
When any characters wear "masks", they inevitably breathe through their mouths.
In a few shots inside of the Psychlo Dome, blue sky is visible at the top of the frame where the dome roof should be visible.
Jonnie drops his walkie-talkie and the camera shows one of his comrades speaking into the walkie-talkie and saying, "Jonnie, the shooting has triggered the alarm! Five guards from the cell, heavily armed and moving fast!" However, his lips are saying something completely different.
Jet fuel has a shelf life of about four years. A fully-fueled jet found after 1,000 years wouldn't even be able to start, much less take off and fly.
In spite of the total breakdown of the society where much of the present-day knowledge has not been passed to the film's present day, the "man-animals" speak perfectly constructed English, including more complex tenses and irregular verbs.
The batteries on those hand-held radios used in the final battle would not have maintained a charge after 1000 years.
Where does the power to supply the electrical devices in the bomber base come from?
After 1000 years of enslaving humans Psychlos have no knowledge of humans including the basics such as culture, language or food.