In the waste disposal chamber, MacGyver removes his shoes to remove his pants. Since the floor fully recedes into the wall, he never gets to put his shoes back on. Yet, while hanging from his pants over the acid, his shoes are on his feet. And later, in the lab, he is wearing shoes as well as instances where his feet can't be seen, but sound effects indicating shoes are heard.
Mac throws Dr. Ludlum's keycard at the laser grid, causing it to vaporize. However, the card can be briefly seen lying on the floor a few inches away from the archway.
MacGyver refers to the entry laser grid as a "20,000 volt laser". This is incorrect as laser energy is not measured in "volts" but in metric "watt" increments.
Mac's watch crystal would be useless for a makeshift telescope.
In the ventilation shaft, MacGyver unhooks a power cable from a box by undoing the clamp on the outside of the box, instead of removing the disconnect inside the box. Later, SANDY (the AI antagonist) "increases power" causing sparks to fly from the end of the cable and the cable to thrash around like a water hose. Electricity simply doesn't work that way.
Sparks would not shoot out of the electrical conduit like they did when Mac Gyver pulled it loose from the junction box. Pyrotechnics were used.
The laser barrier in the hallways as well as the one on the main entrance are superimposed on the TV screen - they move when they shouldn't when the camera twitches.