After Charles pulls the kids out of school and Audie is questioning him outside the barn, her name tag keeps changing between being covered by her sweater, partially covered, and not covered at all.
After Farmer first meets with Mrs. Good, they walk down a school corridor and have a conversation, at which time they pass the same raised and broken ceiling tiles twice.
Farmer is able to communicate with his ground controller, Sheppard, throughout the flight, except when his radio system is not operational due to a malfunction. In fact, radio transmissions are only possible if the antenna of the transmitter has a "line of sight" to the receiver. Farmer could not speak with his ground controller when he was on the other side of the Earth. NASA uses a series of antennas located around the world to receive and relay radio signals to Houston, the home of NASA Mission Comtrol at the Johnson Space Center.
For his first launch, Farmer fuels the rocket with kerosene and hydrazine. Either one can be used as a rocket fuel, but both are worthless without an oxidizer. Even combined, he never would have gotten an ignition, let alone a failed launch.
The capsule is shown firing all three retro rockets at once. The actual retros are fired in a sequence five seconds apart.
The craft's landing was much slower and softer than an actual Mercury landing. A Mercury landing on dry land would most likely have damaged the capsule and severely injured the astronaut.
During the flight, Farmer's capsule comes very close to what apparently is a communications satellite. Typically communications satellites are in geosynchronous orbit 22,236 miles above the surface of the earth. Since Farmer's orbit was planned for 100 statute miles perigee (and presumably an apogee around 175 statute miles, typical for Project Mercury), there is no way he would ever come within sight of a communications satellite.
When the rocket launches, incredibly, the wooden barn remains unburned. In a scene during the second launch, exhaust smoke can be seen coming out the bottom of the barn walls, so it's safe to assume Farmer has designed his barn to overcome the explosive nature of the launch.
The doctor examining Farmer's eye is looking through an otoscope - an instrument for examining the ear canal. He should be using an ophthalmoscope to look into the eyes.
Carnival rides use electric motors connected to huge generators to turn them. When the Farmers have the carnival ride on their property we see a large overhead view of the carnival ride but there is no generator or electrical cord anywhere. The cord is obviously buried and the generator is behind the camera.
When the first, failed launch attempt causes the rocket to tear across the terrain horizontally, the rocket shoots right through a billboard, leaving a hole only about three feet across, much smaller than the diameter of the rocket.
A photo shows Farmer wearing a pressure suit and standing by an X-15 rocket plane, implying he flew it while in the Air Force. The X-15s final flight was in October, 1968... meaning the character would be well over 60 years old.
Farmer's orbital path, due to the rotation of the earth, would not pass over the launch point until 24 hours or roughly 18 orbits have been completed. After nine orbits the path of the capsule would take it mostly over Europe and Asia, then dipping into the Southern Hemisphere, nowhere near the southern U.S. The producers might originally have envisioned a 24-hour flight (and filmed it that way) but for some reason the number of completed orbits was changed to 9 in the script.
Upon re-entry, rockets are fired for the purpose of slowing down the capsule to sub-orbital speed, but the capsule is still traveling many thousands of miles per hour relative to the ground below. However, when Farmer fires his retrograde rockets, his capsule seemed to simply come to a stop, and drop vertically to Earth. In addition, he fired his rockets after appearing to fly over Baja California, for a landing in Texas, while in reality, descending manned spacecraft fire their rockets thousands of miles in advance of their desired landing spot.
When Charlie Farmer launches, the Air Force records an unidentified launch at 29 deg 40 min N by 95 deg 18 min W. This is not rural Texas but actually a spot in downtown Houston.
The orbital views of Africa and Baja California are not accurate for a craft in a low orbit, and would require a much higher altitude.
During some shots of the kitchen area a phone book can be seen sitting on the table. The movie takes place in Texas but the phone book is a 2005 New Mexico phone book.