The clock setting on Geoffrey's barricade changes. When the contest begins, the alarm hand is set to 9 o'clock. When David first connects his frequency modulator, the alarm hand is now at 6 o'clock. The alarm hand then moves back to 9 o'clock right before the door opens.
The pictures of the barricade contest winners changes between shots. One version has Simcic as the winner in the year after Ryman. The other has Simcic as the winner in the year preceding Macgyver.
The dorm room door peep holes show the rooms as visible and magnified while looking through from the hallway. This is the opposite of how peep holes work. They magnify the hallways when looking out from the room, but viewing the room from the hallway would show a very small, miniature view.
David asks about the bomb and MacGyver says the bomb squad is taking care of it, then a few seconds later as they wheel David out, the elevator doors open and Janet comes in looking for David. In real life the bomb squad would have kept the area clear of civilian personnel, and make sure the bomb in fully deactivated and would not let somebody into the blast zone.
When Geoffrey is solving the bolt lock barricade he says that trying to run all 4,096 combinations at an average of 10 seconds per try would take him more than 12 hours. It would actually take 11 hours and 23 minutes.
To stop the bomb Mac Gyver boils the mercury so it becomes a vapor so it wouldn't make a connection with the wires. Mercury vapor is conductive as in a mercury vapor lamp or fluorescent light. Therefore the bomb would have blown up.
The view through David's door peep hole shows daylight pouring through the window, yet it is supposed to be the miniature room model which is being seen - other shots of this model show that there is no light behind the window.
Hillary mispronounces "Chablis" as "Chiblis"
Mac and the Prof speak at normal volume when they discuss their plans to stop David from detonating his bomb. But they do not move away from the speakerphone box, so David would be able to hear them.