Plot hole: Further to the comments about the Lunar Lander being useless as a Mars Lander - who is going to believe that three men spent eighteen months crammed into a tiny Lunar Command Module? Not only would they go out of their minds, where would they store the tonnes of water and food they would need in that tiny capsule? How could the Service Module carry enough oxygen or have enough battery power to make the trip?
Plot hole: The "death" of the three astronauts and the requirement to then fake the whole scenario of the failed mission was obviously unplanned - it came about because of an unexpected computer glitch which reported that they had burned up on reentry, causing a mad scramble to cover up the fake mission and kill the astronauts. Obviously it was planned to have the astronauts "return" to Earth as heroes after their supposed trip to Mars, maintaining their deception (under threat if necessary) for the rest of their lives. One problem. Every scientist on earth would be champing at the bit to get their hands on a sample of Martian rock. Samples would be worth billions, worth far more than Moon rocks are worth today. How was NASA going to explain they didn't have any? They could not possibly fake the rocks - Martian soil and rocks would have a number of identifiable characteristics that a smart first year college student could identify. Using Martian meteorites collected from the Earth's surface won't work, either - prolonged exposure to the Earth's atmosphere would leave tell tale weathering and chemical changes that would be instantly detectable. NASA have painted themselves into a corner and that is not something they would have failed to realise well in advance.
Plot hole: For such a well-financed, well-organised bunch of ruthless killers the people who try to clean up the mess that NASA leaves behind seem to have the intelligence of a cheese sandwich. 'Disappearing' one of their employees - the one who works out the discrepancy in the triangulation of the radio signals - is an obvious necessity but replacing him with a woman who claims to have lived in his apartment for years is stupid beyond explanation. The reporter knows that she is lying - it's as if they wanted to confirm that his suspicions of a conspiracy were true (and hence worth investigating). What is to stop him checking with the man's neighbours, or local shops? What about his bank, credit card suppliers, utility companies, friends and family who would have been in contact with him at that address? What about the landlord, or the mortgage company, or vehicle or driver's licence registration? What about the local electoral roll? There would be official records going back to the day he moved in to the apartment, and neither NASA nor their hired killers could have accessed all of that information even if they knew about it.
Factual error: The whole conspiracy is doomed from the start! They show a Lunar Module on the set representing Mars; the astronauts were supposed to use this to 'land' on the Martian surface. This is insane. The Lunar Excursion Module cannot operate in an atmosphere; it would burn up on entry. It has no heat shield - the engine nozzle and landing legs would have to poke through it if it had. Exterior protrusions like antennae and steering engines would burn off during descent through the Martian atmosphere. While Mars' atmosphere is thin, it is still more than sufficient to burn up a Lander designed this way. All three recent Mars Landers, Spirit, Opportunity, and Phoenix, had heat shields and parachutes to facilitate safe re-entry. This is not a radical redesign of the LEM; it simply cannot be the shape it is if it is to work in an atmosphere. Any schoolkid would know that, and the world's media would not be fooled for a second.
Factual error: If one person (at NASA) was able to calculate the distance between the returning Mars capsule and Earth based on their radio signals, then everyone with basic radio receiving equipment would be able to. The Russians routinely track American spacecraft and publish details of their trajectory in Pravda, and amateur astronomers throughout the world do so, too. This all comes from triangulation of their radio signals. There is no way that NASA could hide this simple fact from their worldwide audience.
Other mistake: After the crash landing in the desert, when the astronauts are preparing to head out on foot, Brubaker states that he will continue west, then tells Walker to go north, and Willis to go south. Brubaker heads out straight ahead, Walker goes to the left, and Willis to the right, meaning that Walker was actually going south, and Willis to the north. (01:04:40)
Plot hole: How did Brubaker and Caulfield make it past the secret service into the graveyard for the crowd to see them? If the President and Vice President are in the graveyard for a funeral there certainly would be heavy security. Especially disheveled, without identification, bringing in a civilian vehicle that could conceivably be used as a weapon in a crowd.
Visible crew/equipment: When Brubaker hides out in the Petrol station, the two helicopter pilots approach the window. A reflection of a member of the crew wearing glasses can be seen reflecting in the window where the pilots stand.
Revealing mistake: Just after the helicopters crash during the chase with the crop duster keep a close eye and one of the helos is still in the shots flying.
Plot hole: Somehow, Elliot Gould and James Brolin drive several hundred miles through a desert and halfway across the country in Gould's car (a Datsun 280-Z)in a matter of a few minutes, to arrive at Brolin's supposed funeral in Houston, Texas revealing the conspiracy. I used to own a 280-Z and they are not that fast.
Visible crew/equipment: During the helicopter chase sequence with the cropduster, the shadow of the camera helicopter that is filming the chase can sometimes be seen.
Continuity mistake: In the scene at the remote gas station, after Brubaker has entered the office, he goes through the cash register which is located at the end of the counter [viewer's right]. A couple of shots later, after breaking into the Coke machine, and while he is at the pay phone, the cash register is nearly a foot to the viewer's left on the counter. Also the coin box from the Coke machine is to the right of the cash register on the counter. In the previous shot when he turns from the Coke machine to go to the pay phone, you see the end of the cash register without the coin box in the way.
Factual error: In the beginning of the movie, a Saturn V is seen representing the launch vehicle that will take Capricorn One to Mars. This is downright ridiculous. A Saturn V's third stage (that would insert into orbit and make the injection burn) does not have nearly enough Delta-V to make a Trans-Martian Injection from low Earth orbit.
Revealing mistake: When the Lear jet is getting ready to make the emergency landing in the desert, James Brolin calls for full flaps. As we see the jet land, we can see that the flaps are indeed down. When the dust clears we see that the jet has made a wheels up landing since they lost the left gear on take off. However, the flaps are up.
Continuity mistake: Astronauts are escaping in desert. The one who survives cuts off piece of material from bottom of his left pant leg. He ties material around his head like a headband. Later he is standing and it looks like left pant leg is uncut, and he's wearing the headband.