In actuality, training on the Lunar Lander Training Vehicle (LLTV) was not a standard part of an astronaut's training. The only astronauts who trained on it were ones earmarked for a role that would require them to land on the Moon. For example, Neil Armstrong flew it many times to train for Apollo 11, but neither Michael Collins nor Buzz Aldrin flew it at all because their roles didn't require that training.
In the flashback scene where Tracy first meets Gordo at the airport before they go flying together, he's wearing a regulation US Navy flight suit with a single gold bar ("butter bar") on his shoulder, making his rank Ensign (O-1). Yet the patch on his chest designates him as LT, USN (O-3).
When Gordo notices the plume of black smoke in his rearview mirror, he immediately does a U-turn in the road. While he's driving toward the airfield, you can see the road markings showing that both lanes go in the same direction. He's essentially heading into possible oncoming traffic.
When Tracy and Jodi share a bottle of water in the desert, you can clearly see the bottom of the bottle when Tracy tips it back to drink. You can see a plastic resin identification code (the number within triangular arrows) imprinted there, though that numbering system wasn't introduced until 1988, much later than when this takes place in the 1960s.