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: 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: 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.
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.
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.