Factual error: Bozer and for that matter I would assume all of the team went to a spycraft academy. A basic subject in any of such academies is surveillance, including proper techniques to follow and stake out someone. Bozer being so inept at tracking MacGyver's father is inconceivable given their training.
Character mistake: MacGyver is explaining the jamming of a tracking signal. He states that the tracking device is emitting an RIDF signal. He should have said an RFID signal. (00:26:20)
Factual error: A US Pilot's License is shown. It is pretty much all wrong. Salient among the errors is that US Pilot's Licenses do not have a picture. The nationality should be USA not America. They are green fading to white, and not blue. It does not have a hologram of the FAA seal. The signature on the front is that of the pilot and not the FAA Administrator. I realise that it would be improper to show an actual license on a TV show, but this is so far off as to be ludicrous. (00:02:20)
Factual error: MacGyver and Russ are bringing two large oxygen cylinders into a room. From the way they handle them to get them off the cart and onto the floor, you can tell they are empty. To make matters even funnier, MacGyver manages to break off the valves on both tanks at the same time with just one stomp of his foot. That is physically impossible. Continuing the farce, the tanks pretty leisurely rocket away, lifting all present slowly to the skylight. I have seen a video of just one small air tank break a valve. It shot across the room, through the wall, flew through the air, and embedded itself three feet in the ground over 40 feet away. Believe me, not at all how depicted here. (00:35:20 - 00:36:20)
Factual error: Mac's "cutting torch" was supposed to weaken the lock, and the pressure difference would do the rest, since there was "no air in the room." However, the door swings outward. If there is no air in the room, the higher pressure outside the room would keep the door closed, working against him, rather than for him. Besides this, the arc from a 12v car battery is unlikely to considerably weaken a steel lock. (00:01:15)
Factual error: MacGyver is wearing what is supposed to be a US Navy uniform. But he has the shoulder epaulets of a Lieutenant Commander, and is wearing a Chief Petty Officer service cap. (00:00:30)
Factual error: MacGyver is using an improvised cutting torch to weaken a lock on a door. When he thinks he has cut enough he drops the torch and immediately holds on to the lock to open it. If It has been subject to a cutting torch long enough to weaken it, he would not be able to grasp the lock with his bare hands without seriously burning them. (00:15:00)
Factual error: All the information regarding Germany and there train system are wrong. All the fast trains (InterCity Express) in Germany are electrified and therefore no-one could land on the top of the train with a helicopter. Also the trains have a completely different design and the train station in Berlin and Frankfurt have a completely different look.
Plot hole: The team is trying to recreate the movements of a murdered seed vault employee by using his phone's geolocation attributes (compass, accelerometer, altimeter, etc). They are trying to backtrack from the place they found the murdered employee to where he first surprised his killer. They backtrack using the data from the employee's phone, and there is another set of data shown on the computer. But they only have one phone's data to work with. Where did the data presumably from the killer's phone come from? (00:12:50)
Factual error: MacGyver attaches a hose from a car gasoline filler port to the jet engine from a crashed plane. He uses a makeshift lever and the engine ignites. 1. A crashed jet engine has an astronomically low chance of working. 2. A jet engine runs on essentially refined kerosene with some additives. Automotive fuel would be useless. 3. The hose used to "provide fuel to the engine" is not siphoned to provide a usable flow of gasoline. 4. The braided wire hose is quite a long piece. It just happened to be lying there completely free of any holding clamps or terminations? How would just one piece of a long hose become free of the airplane? 5. The engine is not attached to anything, but the thrust of the lit engine does not move it one inch. 6. Even after being lit, it does not set fire to anything in spite of being in the middle of a lot of combustible material. (00:13:15)
Continuity mistake: In the first scene a pot on the stove has boiled over, spilling down the sides. In the next scene, the pot is about 3/4 inches from the top with no spillage. In the succeeding scene, it is once again overflowed and spilling down the sides. (00:03:05)