When Luther asks Ramón about the death of his brother, Luther's hands are laced in front of him when the camera is on him, but holding Ramón's jacket when the camera is on Ramón.
The piece of fabric that rips of of Tommy's coat that sticks to the tree branch is in a different position when MacGyver comes across it later. When it is first shown, it is snugged securely between a crack in the branch. When MacGyver finds it, it is more or less just resting on top of the branch.
Though the plane's registration number on the outside is N761C, the in-cockpit view shows a dymo label with the registration as N739GA.
Two different planes were used. The lettering style of the N-Number differed after it was seen crashed on the ground.
Mac plots the runway due west. This ends with several tall trees that he would have to avoid. He should have picked the longest run and aimed for the minimum obstructions. However, taking off into the wind is the preferred option, as a much shorter runway is needed. Material moving on screen indicates that the plane is indeed taking off into the wind.
When the plane starts a nose dive and McGyver has to get the plane under control, they show the altimeter dropping until it nears 1000 ft. But the view out the diving plane's front window shows they are about 1000 ft over hills. Altimeters measure from sea level, so the plane should have crashed long before the 1000 ft reading. Based on aerial scenes from the show, those hills had to be at least 3 to 4 thousand feet high.
At about the 24 minute mark, as the cougar is running away from the shower MacGyver just gave her, there is a brief glimpse of a woman's head over the rocks on the right hand side of the screen. Most likely, this is the animal handler.
The plane is fitted with a front runner to replace the wheel. After takeoff the front runner has a wheel.
When taking off from his improvised runway, Mac fails to extend the plane's flaps. Flaps are extensions on the wings used to increase lift and drag. This would let the plane take off at a slower speed and steeper angle. Both are very important due his high drag nose skid and the trees at the end of the runway.