When the Firefox flies over the Russian cruiser which is then seen firing missiles at it, the cruiser is obviously an American cruiser, probably the Belknap Class.
When Baranovich asks Gant if he smokes, Gant replies, "Not for years," yet earlier in the film he was smoking a cigar at the bridge.
The Firefox rolls over the same guard twice when blasting out of the hangar.
When Gant gives the command to fire the missiles, he uses the command "skaitie pierva rakieta" which translates roughly as "Launch First Missile." However, this is the only command that is given (i.e. he does not give a command to launch the second, third, or fourth missiles) to launch all his ordinance. Earlier in the film, the weapon system is explained as thought-controlled (but only in Russian), so perhaps he is vocalising an order in order to marshal his thoughts.
After the explosion in the hangar, you can see Mr. Gant in the shower during the alarm. A few moments later he's seen in his pilot's uniform heading toward the "Firefox". It's very unlikely that Mr. Gant can go from the shower to wearing a pilot's uniform in the hangar area in such a short period of time.
After the Firefox is stolen, General Vladimirov explains to the First Secretary that in order to maximize fuel range, Gant will have to control his speed and fly low to conserve fuel. The part about controlling his speed is true enough: speed, particularly with afterburners, is the enemy of fuel consumption, but flying low is exactly the opposite of what he should do. Airplanes - jets, in particular - burn far less fuel at higher altitudes where the air is thin than down low where it is much denser.
Through all the movie Soviet officials keep demanding papers - VASHI BUMAGI (your papers), whilst correct way to demand them in Russian is VASHI DOCUMENTY - your docs (ID).
The term First Secretary was only used from 1953 to 1966 for Khrushchev and Brezhnev. Prior to and after those years, the correct term was General Secretary.
When the US submarine, code name "Mother 1" surfaces, you see an underwater shot of the vessel pushing out air from the ballast tanks in order to surface. This is actually the exact opposite of how a submersible works. Air would not be taken from the ballast tanks but instead pumped in.
Russian words on Firefox's screen related to the ammo are messy and the last one has nothing to do with it.
When taking off from the ice floe, the Firefox has its air brakes fully extended, a highly inefficient way to take off.
After one of the metro trains pulls out of the station in 'Moscow', the German word 'KURZZUG' (=short train) is clearly visible on the wall behind it - indicating that a German-speaking country (in fact Austria) was used to double for the USSR.
After the interrogated detainee is 'killed' during the interrogation, one of the veins on the actor's neck highly visibly continues to show a pulse.
When Gant is walking towards his hotel (Moscow) we can see Red Square with St. Basil's cathedral at the background which is obviously a picture, not a real thing, and of poor quality besides. Moreover, there's no hotel by Red Square in the direction he was walking. Hotel Moscow is situated at the opposite side, about 2km distance from the point of "shooting".
On the way from the airport several non-Soviet cars are visible parked one by one along the road. Highly unlikely in '80s USSR.
When the Russian Hind helicopters fly over Mother 1 (US sub in the Pole). The close up of the Russian cockpit is actually the airframe of Blue Thunder, not a Hind.
Whenever the Firefox launches a missile, it shows a single launch from the Firefox's weapon's display, yet from the target view, two balls of light representing the missiles are showing - no air-to-air missile, known or unknown, can split mid-flight, let alone track the same target twice.
When Gant and Voskov are flying their respective MiG-31's, no seat harnesses are visible on their shoulders. Flying a high-performance supersonic aircraft is not possible without an adequate restraint system on the pilot seat (not to mention providing for a parachute attachment, should an ejection be necessary).
When he exits the subway you can see on the other side still written "Suedtirolerplatz" and you see a map of the Vienna subway net.
When the Soviet "hotline" phone sounds in an extreme close-up, we see the GTE logo on the bottom of the phone...
The speaker phone box in Col. Kontarsky's office has AT&T on it, highly unlikely in the USSR.
When driving away from the airport, there is a sign from an Austrian automobile club visible for a short period.
There's no Kirov str. within walking range by Kolomenskaya metro station.
After the Firefox has landed on the ice floe, he asks the sub commander to steam off a 3,000 foot runway in the three minutes he has until the Soviet investigative forces arrive. There is no way that the sub crew could steam a section of ice that long in three minutes, let alone go back to the sub, find the hoses, hook them up, let alone have 3,000 feet of steaming hose, let alone having enough pressure to do the job.
The entire performance of the "thought guided" missile system that was highly touted was never realized as the breakthrough it was, albeit it totally unrealistic. His contact inside the U.S.S.R. even said, "now, you don't even have to push a button...", yet in the first battle scene inside the Firefox, Gant is manually arming the weapons systems, with the gun firing (red) button, no less. Additionally, we are told at the beginning that the "sensors inside the helmet" automatically seek out and detect threats according to the pilot's thoughts, yet in the final scenes, it is a long, drawn-out dogfight. If what was true about the thought-guided threat attack system, the second prototype that was attacking Gant would have never survived after the first missile attack. Instead, Gant is taking evasive action for minute after minute, needlessly flying through mountains, doing barrel rolls and all kinds of acrobatic maneuvers. Yet, he did not think to launch the "rearward" missile until after he recovered from his flat spin by lowering the landing gear?
Stealing the second prototype instead of the first one would have been a better idea seeing as the second prototype can refuel in midair but the first prototype can't and blowing up the hangar with the rear defense pod would guarantee the destruction of the other prototype.
Gant knows that he is supposed to be flying subsonic to conserve fuel and also remain undetected by the Soviet system that can plot sonic booms, yet he advances the throttles more than once to "see what the airplane will do."
When Col. Kontarsky receives the sketch of Gant he recognizes "him" as the "GRU Officer" who confirmed the order to have the dogs search the tree line. GRU Officers were members of military intelligence and wore the standard uniforms of the Soviet Army, Red insignia and piping for most Army officers and light blue for Airborne. Yet Gant/Eastwood is wearing the same dark blue colors, only worn by the KGB, as Kontarsky. No KGB officer would mistake their own uniform for GRU. Additionally, GRU had no internal security function and held a deep rivalry with KGB, making it highly unlikely a GRU officer would be allowed near any KGB guarded project like the Mig-31.
When Dr Semelovsky arrives at the checkpoint, he turns up late and a guard asks him why, the response from Dr Semelovsky is that the car broke down and the guard then checks the engine and comments that is filthy. The error is that when the guard asks to check the engine, he says "open the boot" instead of "open the bonnet" (where the car engine actually is).
When Aubrey briefs Mitchell Gant about the homing device, he mentions that it will pick up Mother-1 within 100 miles. However, on board the Firefox when Gant's homing device picks up Mother-1, he is over 140 miles out.