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.
Continuity mistake: There is a scene at an airport where Mel Brooks is approached by a man claiming to be a FBI agent or something like that. In the next shot inside the bathroom you can see the boom microphone from the top of the screen. (00:04:05)
Factual error: After the plane is submerged, Jack Lemmon says, "... this plane is pressurized!" Jet aircraft are pressurized by bleeding air from the compressor sections of the engines into the cabin; in other words, the plane is only pressurized while the engines are running. Also, aircraft are only pressurized to a few psi above the outside air pressure at altitude, and never to more than the air pressure at sea level. The water pressure would be a great deal higher than the air pressure in the cabin, and since aircraft are not water tight, the water would quickly fill the aircraft. (If the aircraft was in 50 feet of water, the water pressure would be 21.7 psi, versus a maximum cabin pressure of 14.7 psi.)
Revealing mistake: The shot of the two nuclear missiles being launched is used twice, just reversed. They seem to have changed the saturation slightly in one of them to make it look different, but there are identical clouds at the top left/top right in both shots, ruining the trick.
Continuity mistake: When the crew hauls the female orca aboard the boat, the harpoon line is wrapped around her entire body several times. When they cut the rope and drop her into the water, the line is wrapped only around her tail. When the male orca is pushing her at sea, the rope is again wrapped around her entire body.
Factual error: After mounting armor in the bus they are approaching Phoenix on a two lane highway from the northwest. When entering the city they are shown coming around South Mountain on Interstate 10 from Tucson from the south.
Visible crew/equipment: During the opening scene when the boat is being pushed ashore you can see the shadow of the boom mike in the water's edge.
Continuity mistake: When Pat is attacked on the stain glassed window near the start, she has blood on her right cheek. When she is then dropped and hung, the blood stains are different. (00:12:20 - 00:13:00)
Factual error: Donald Pleasence's character makes a left turn at an intersection controlled by a traffic light. The camera pulls back and reveals an Interstate highway shield on the road he turned from. Interstate highways never have at-grade intersections controlled by traffic lights; they are designed to be non-stop routes with access to side roads available only through ramps and grade-separated interchanges.
Plot hole: When the bomber is surrounded at the end he gets shot in the leg but manages to get away from all of the police that were surrounding him. They were literally an arm's length from him.
Visible crew/equipment: When 'The Car' catches the truck, it tries to shove it off the road. The 3rd attempt happens as the Car gets very close to the camera, then veers across the screen, our left to right. The clear shadows of several crew members aboard the camera truck are visible on the front of the Car. (01:24:50)
Continuity mistake: In the opening scenes, when David is chiding Gail for grabbing him through the porthole of the wreck, his right hand is gloved, then ungloved, then regloved..all in the space of a few moments.
Visible crew/equipment: After Bruno Ganz shoots the man in the train station he walks out onto an open-air concourse. In the overhead shot facing him, we can see the strip of duct-tape on the ground marking the spot where he is supposed to stand.
Factual error: After loading the bomb, Dern and Keller hijack the blimp. As Shaw watches the blimp heading for the stadium, he spots a helicopter across the field, moving bundles of pipe. Shaw and Weaver commandeer the chopper to chase down the blimp. A major part of the security plan for the Superbowl, was that the only aircraft "trusted" to be allowed to fly within a 100 miles of the stadium are the Goodyear blimp and the Police helicopter. The other helicopter would not have been allowed to fly that day.
Continuity mistake: When Guido carjacks the Citroen, he pushes the driver off the seat in a spot entirely in the shadows. In the faraway view you can see he starts driving in a spot with the asphalt in direct sunlight. (00:10:50)
Continuity mistake: When Regan and Bianca first jump on the bus to escape the hitmen you can see through the windows that there are only six people on the lower deck, but when the scene changes to inside the bus all the seats are full. (01:00:24)
Suggested correction: They could use meteors that had landed on Earth. This is one of the theories for the "faked" moon landing, that they either created the moon rocks from scratch, or collected meteors. As for the death of the astronauts, that's not a plot hole, it's the plot of the movie; the powers that be wanted the men to fake everything and return as heroes. When they wouldn't play along, it was decided they needed to be eliminated.
It is clear from the narrative of the film that it was planned that the astronauts would "land" safely. Using meteorites would not work - exposure to the Earth's atmosphere would mean (and has meant) that the rocks would show weathering and chemical changes that anyone would be able to detect.