When Martin and Edel get back in the car at the gas station the hose and nozzle are still in the car's gas tank. When they drive off the hose is gone and the gas cap cover is closed.
Moritz drove a W123 version of Mercedes-Benz on their way to Brussels, including the fuel stop at the border. However, the interior shot of Mercedes-Benz used during the detour in the city was a R107 version (three round ventilation nodes on dashboard). Mercedes-Benz that Moritz and General Edel climbing out at the detour is a W116 version.
The placements of windscreen wipers between interior and exterior shots at the detour switched from left to right, denoting R107 and W116.
At the gas station, Martin leaves the gasoline nozzle in the tank when he rushes to meet Lenora. The nozzle is still visibly inserted into the passenger side tank when Martin returns and enters the driver's side. General Edel enters the passenger side without remarking on it, and when the car pulls away the nozzle is no longer attached.
For vehicles of the German army (Bundeswehr), a car radio would have been forbidden.
During the combat exercise in the woods, although it appears to be an NBC exercise (Nuclear Biological Chemical) to test combat capability during any of these extreme conditions, the soldiers involved in the maneuvers were only wearing their gas masks and gloves and not their entire NBC suits, to include their hoods and special rubber boots, thus making the point of the exercise pointless.
When displaying the encoded data on the stolen floppy disk they accidentally display the program that created the codes. This program was written to generate random codes showing that the codes displayed are random nonsense they're not encoded secrets.
When Martin and the General are filling gas at a station, Martin drives away without removing the gas pump nozzle.
When the East Germans examine the stolen NATO floppy in an IBM computer at Dresden University, a number of rows of 5 six-digit numbers is printed on screen. This leads them to conclude that the disk is encrypted. However, the BASIC program that prints the output is clearly visible on screen too. This shows that the output is not read from disk but generated by a program.
When Martin sneezes due to cat allergy, he does so into the crook of his elbow. This was not done in the 1980s - in fact, it only became common in the 2000s, after it was found that doing so was the best method of preventing the sneeze from broadcasting droplets in case of viral infection. In the 1980s, people would sneeze into their hands.
In the third episode, set in 1983, there is reference to the IBM 486 computer. This model was not introduced until 1989. The model mentioned was the IBM 436 (and IBM 567) which are both fictional. The Robotron 5120, despite sounding fictional, was available from 1982.
When the East German IT expert is using the IBM computer the "BASIC" computer code used to generate / display the coded message is visible.
In 1983 all German cars had DIN license plates. Nowadays they use to have Euro plates with special FE font - except Bundeswehr cars which carry plates beginning with Y and the German flag still using DIN letters.
In this episode they use a plate with FE font for a Bundeswehr duty car. Also the flag comes first followed by Y a dash and the number which is in another order.
When General Edel visits a prostitute, a Citroen BX is seen parked in front of Edels Mercedes. The BX is the face-lifted version that entered production in August of 1986 (model year 1987). A 1983 BX would have had orange turn signals by the headlights, not transparent.
When Sylvester Groth's character sits down (21 minutes into the episode) while talking to the technician, the radio mic transmitter the actor is wearing is clearly visible under his costume.
Martin and the General drive from Bonn to Brussels along long country roads... why would they, given that the fastest route would have been to take the Autobahn from Bonn via Cologne and Aachen straight on to Brussels (crossing the border at Lichtenbusch)?