Continuity mistake: When the Golden Eagle is shot with the crossbow by the man, It goes through it's wing. Later when MacGyver comes to try and take it out, it is in a different position on the bird. It is not through the wing anymore. (00:07:25 - 00:09:15)
Continuity mistake: While running on the mountain, the stunt double is wearing a white shirt while MacGyver is wearing a blue shirt.
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.