A well-trained astronaut would not carelessly take off a glove to plunge a hand into unknown soil not knowing what chemicals or organisms would be in the dirt.
When the spaceship jettisons its tanks upon entering the Martian orbit, the tanks burn up in the planet's atmosphere. In fact, the Martian atmosphere is so thin that there is little friction to so thoroughly destroy an object falling into the atmosphere.
The crew uses Martian "snow" to replenish their water tanks. From what is known now about Mars, the snow would likely be dry ice flakes and would have produced the gas carbon dioxide when they sublimed, not water.
Radio transmissions from Earth to Mars would take approximately 4 to 20 minutes one way (twice that for a reply) depending on their positions in orbit.
In most shots of the "Wheel", it is shown turning counter-clockwise. But in the scenes of Cooper being transported to it after becoming paralyzed aboard the rocket, the Wheel is suddenly turning clockwise - until the final shot of the rescue craft heading toward it, where once again it is moving counter-clockwise.
When Captain Merritt enters the ship as his father is emptying its tanks, he's wearing a spacesuit and has to close the ship's hatch before getting out of it. Yet the entry to the engine room below, where his father is, is completely open, exposing his father directly to the lethal Martian atmosphere through the ship's open hatch.
Despite the zero-G conditions on 'Spaceship One' (hence the need for magnetic boots), many objects are clearly under the influence of gravity (e.g. the safety-belts, the bookmark ribbon on the General's bible).
When the engines are turned on during the asteroid scene, strings can be seen holding up the ship.
When the spaceship blasts off from Mars for the return trip, at the moment that the Captain shuts off the motors, because they have reached escape velocity, the Space Speedometer is pegged on zero MPH.
The transparent image of an effects crewman can be clearly seen to the right of the screen, hunched over, pulling Siegle and Fodor during the antenna repair sequence just before the asteroid hits.
The transparent image of what appears to be the flying rig can be seen moving towards the upper left as the floating body of Fodor drifts after being struck.
Visible wires during virtually all of the anti-gravity and space suit sequences, but particularly visible attached to the helmet of the suit when the unconscious "Mahoney" is laid on the floor of the ship.
The astronauts all wear spacesuits on Mars, yet take off their gloves and handle the Martian soil bare-handed, exposure which would in reality destroy their hands and probably kill them.