In the opening scenes in the mining levels, human voices are heard through the radio links, but ambient industrial noise is heard "in the clear". In a vacuum there would be no such noise. If the noise were heard from the miners' perspective (as was the radio chatter) it would have been low frequency noise from mechanical contact with the ground and manual equipment only.
When Spota is shown walking through the locker room he passes behind a man wear a red hat as he open his locker to change before continuing further down center aisle. A few seconds later Spota is shown passing behind the exact same man (now shirtless and with no hat) a second time. While it's possible that Spota doubled back it is unlikely because he is shown entering both shots from the same direction. if he had doubled back he would have been coming from the opposite direction in order to pass the man the second time.
Io is located within the Jupiter's radiation belt and receives about 3,600 rem (36 Sv) of radiation per day. This is approximately ten times more than what is considered to be a lethal dose for humans (estimated to be 400 to 450 rem (4 to 5 sieverts) received over a very short period). Therefor it is highly unlikely that a permanent settlement on IO would be possible even with heavy radiation shielding. Also people are seen in the movie working for extended periods outside on the surface of IO. This would also be highly unlikely due to the intense radiation from the Jupiter.
In the outdoor scenes showing Io's mining buildings with Jupiter and the stars in the background, the stars are blinking. Such blinking is caused by viewing the stars through an atmosphere, as on Earth. But Io has virtually no atmosphere. Therefore, the stars should have been shining steadily.
When O'Neil is wandering around outside, he experiences 0g, while those inside experience 1g. This is most obvious as he drops the panel outside the greenhouse, and again as he rigs the tunnel to explode. Gravity isn't contained by walls or doors, and isn't dependent on air pressure. If the people inside have gravity, then it also exists outside, and O'Neil wouldn't have been floating around.
In the opening sequence where "computer readouts" across the bottom of the screen set the scene, one of the last of these identifies the Io mine's "Principle Ore: Titanium" instead of "principal". Also "marshal" is misspelled as "marshall" (but "dependants" is the usual UK English spelling of "dependents" and is not an error).
When O'Niel finds the corpse in the zero-G cell, blood is shown dripping upwards. In real zero gravity, the blood would be propelled in whichever direction it was forced out of the body. With a corpse, it would simply stay in the body.
While Marshal O'Neil is outside in his pressure suit, he walks and runs normally, as if he was on Earth. But since Io has only a fraction of Earth's gravity, he should have been moving in slow, hopping steps similar to our astronauts on the Moon.
The shuttle carrying the two hit-men arrives 42 minutes early on its 70-hour trip from the space station. Since the laws of physics couldn't have been broken, this means that someone made a huge error in calculating the orbit of the shuttle (all objects in this case are in orbit of Jupiter), but by blind luck still managed to intersect with Io anyhow. If the shuttle HAD arrived on time, Io would have been in a totally different position, as it moves at 17.3 km per second due to its low orbit around Jupiter. The only way to arrive early would be to expend a lot more energy, which would mean lost money for Con-Am. (Even then you would still know the exact time of arrival - it's just physics.)
The terrestrial atmosphere of the studio is evident even though the exterior scenes take place in the near-vacuum of Io. When O'Niel drops the panel atop the greenhouse, it flutters away from him instead of falling straight down. The gunman shoots at the panel through the greenhouse window, breaking it, and the resulting explosive decompression causes a billowing cloud of gas and debris. Nothing "billows" in a vacuum, the surrounding air allows that, so the gas and debris should have sprayed away from the greenhouse in more or less straight lines.
In one of the opening shots, when we first see the mining complex on the surface of Io and Jupiter in the sky above it, the sunlight hitting the complex is clearly coming from the left side of the screen, but Jupiter is lit from the right side.