Continuity mistake: Throughout the desert car chase, the bad guys' Chrysler hood ornament and various hubcaps on different wheels of their car disappear and reappear multiple times. The car is dirty and then clean too.
Visible crew/equipment: Early in the episode a thumb/finger is visible at the bottom of the screen turning the timer wheel simulating a working timer that is actually just a dummy prop, a few seconds before it explodes. (00:02:39)
Factual error: A 250-year-old sea chest recovered from the ocean floor is opened, and all its paper items are perfectly dry: the log book can be opened and read, and the letters can easily be unrolled. Highly unlikely. The chest's wood and pitch would deteriorate (salt water is extremely corrosive), and the paper should be damp and crumbly, at the very least. Even more likely, it would have become a lump of unreadable sludge.
Continuity mistake: When Mac and the ambulance are running through the checkpoint at the hospital exit, when you first see the shot the stop bar is already broken off on his side of the road, in the next shot they are driving through the bar breaking it off.
Ghost Ship - S3-E4
Visible crew/equipment: MacGyver is repairing the broken boat to get to the abandoned ship. When he leaves the shore and starts to paddle towards the ship, you can see a boom mic drop into the picture from top left. (00:09:15)
Continuity mistake: MacGyver appears to be a novice at mountain climbing, but in the very first episode he mountain climbed like a professional.
Continuity mistake: In the scene where the gang are chasing after the two kids, it is raining and the street is wet. They stop chasing and turn around when they see a police car go by. In the first shot of the police car, the street is completely dry. (00:05:45)
Continuity mistake: The episode begins with MacGyver's Jeep having a blowout and going off the road, however, when we see the overturned Jeep, all 4 tires are inflated. (00:01:45 - 00:02:15)
Continuity mistake: Here as in every episode where MacGyver's Jeep appears, it's the '80s model with the square headlights. When we see him fixing the Jeep after the wreck, the headlights (or at least the holes left by them) are the older round ones.
Answer: Late one night, Geoffrey used a covert listening device to overhear David explaining his barricade device to Janet which is how he figured it out.
How do we know Geoffrey really did use a covert listening device? They didn't mention him using one.
There was a scene of him using it when David told Janet about his barricade.