When MacGyver is trying to fix the landing gear we can see that the plane is flying over a city complete with streets and houses. Then when Mac parachutes out they are suddenly over a rural location.
Jack Dalton lowers the landing-gear by moving a long metal valve-handle on the instrument-panel in front of him, but then when he tries to "cycle" the gear to get the balky left wheel to lower, he uses a ceiling-mounted switch.
Jack turns his pilot's hat around backwards when he tells Katie that he's "the mad rover", yet in the next shot as he heads to the fridge for another beer, his hat is facing forwards again.
When Mac looks down through the wheel-bay at the ground below, houses and trees can be clearly seen, indicating that the plane is flying fairly low. Yet when he later parachutes out of the plane after freeing the stuck wheel, the ground is a lot farther away, with only "faint and vague checkerboard-pattern" outlines of properties and roads. Jack Dalton could not have ascended to a higher altitude because he had only one operable engine and the flaps were stuck; in fact, the plane was descending rapidly, as indicated by the altimeter.
As revealed in the 1967 Stockport Air Disaster, a non-powered propeller that is not feathered will "windmill" and thus create a lot of drag, even for a four-engine plane. So if one of only two engines on a plane failed, the plane would totally spin out of control unless the prop was feathered, but Jack makes no mention of doing this.
A bottle of beer is shown falling over and pouring the beer on MacGyver's computer keyboard. This is then shown to short out his computer. While the beer could have shorted out his keyboard, none of the beer got on or in his computer and could not have shorted it out.
The sign for the Officers Club is missing the apostrophe (should be spelled Officers' Club).