The astronauts are told that the atmosphere on Mars does support (human) life and that no helmets are needed. In reality, Mars' atmosphere is 95% carbon dioxide and only 1.6% oxygen, making it incompatible with unprotected human life.
The second Mars expedition uses "instant communication" by laser to get rid of the time lag in communicating with Earth. According to Einstein's theory of special relativity this is not possible.
When the first astronaut ventures onto the Martian surface, he casts multiple shadows (presumably from overhead lighting on the soundstage). On Mars, however, all light would come from the (more distant) sun, so that all shadows should fall in one direction.
The sand shark just misses the bloody gloves it aims to devour, revealing that it is, after all, a hand puppet performed by a puppeteer who can't see.
Misuse of Latin. Col. Danvers says "No one saw the enemy, i.e. (that is), invisible." when he should have said "No one saw the enemy, ergo (therefore), invisible."
Vertical seams or creases can be seen in the backdrop of some of the views of the Martian landscape.