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.
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.
The movie claims that gold is the most precious metal the aliens are after. A quick study of Earth economies before the destruction of the planet would have revealed that central banks store gold as counter value to issued currency. Instead of plundering these depositories the aliens resort to a laborious mining technique and ignore the stored gold for a thousand years.
In the remains of Denver, ruined for 1000 years, Johnnie finds books in good condition despite being in the open air, cars with still-pressurized tires and wrecked buildings with completely intact plate glass windows.
Terl tells Johnny that soldiers with their technology only lasted nine minutes against the Psychlos, yet untrained cavemen were able to defeat them using the same technology (which had been sitting unmaintained for 1000 years).
Much is made of the alleged inability of "Man-Animals" to mine, yet there is a scene in which many of them are seen operating a forge, which requires know-how exceeding the simple act of digging for gold.
After spending time in the Knowledge Machine, Jonnie learns the Psychlo language and many other things, specifically including mathematics. Somehow this also teaches him terms such as "Euclidean geometry" and enables him to translate that into the English of an uneducated, primitive human culture as well as to read English texts, despite the fact that the Psychlos appear to have no knowledge of English.
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.
The goof item below may give away important plot points.
The nuclear device is around 1000 years old; at this age key elements of the device would decay and need to be replaced, including the radioactive metal initiator, which would require a working nuclear power plant to replace. This is a serious plot hole considering the Psychlos' aversion to radiation.