After Major Kong lists the contents of the emergency ration kits, he says "Shoot, a fella could have a pretty good time in Vegas with all that stuff." His lips are saying Dallas instead of Vegas. President John F. Kennedy was assassinated in Dallas shortly after filming was completed, and the producers did not want to remind anyone of sad events during a joke.
When Mandrake finds the radio, it is on the shelf of an IBM 1403 high-speed printer, with the cover open. The printer is running; anyone who has ever been around a working 1403 printer knows that they are very loud. Operators had to shout to be heard. The printer is not making the loud noise it should be making while running in the shown 600 lines per minute mode with the cover open.
Towards the end of the film, when Strangelove is fighting with his renegade right hand over control of his wheelchair and punches it several times out of frustration, the Russian Ambassador (Peter Bull) clearly corpses (laughs) at Peter Sellers' performance and then quickly regains his composure.
De Sadesky says that the fallout from the doomsday device has a half-life of 93 years, but then he also says that the fallout would circle Earth for 93 years. This is a contradiction: half-life is the time it takes for radiation to be halved, not completely dissipated. It is common however for people to confuse these concepts, and the dissipation time for the fallout from a nuclear weapon salted with cobalt is indeed about a century.
De Sadesky claims that the doomsday device are large nuclear weapons that have been jacketed with a compound of Cobalt and Thorium. While Cobalt is indeed a first choice when making such a weapon, using Thorium makes no sense at all since it will not be activated by the blast to form any dangerous fallout.
General Turgidson tries to dismiss de Sadesky's claim of the doomsday device by saying radiation from a nuclear fallout is "down to a safe level after two weeks". But the idea of creating so called "salted" nuclear weapons by using cobalt in them was put forth by Leo Szilard - the "father of the atomic bomb" - already in February 1950, and it is this concept that doomsday device in the movie is built on. The general would be well aware of salted bombs and their capabilities in 1963 when the movie takes place.
When Gen. Ripper and Capt. Mandrake are using the belt-fed machine gun, in one shot Mandrake is holding a chair over his head for protection, but when it cuts and the camera is behind them and Ripper crawls away from the window, Mandrake isn't holding the chair, and the closest chair is 10 feet away from him.
General Turgidson learns from his secretary, Miss Scott, of General Ripper's ordered attack on the USSR at 3 a.m. Washington D.C. time. However, the concurrent scenes at Burpleson Air Force base (somewhere in the Western United States) take place in the daytime.
When General Jack D. Ripper is firing the .30 caliber machine gun with the assistance of Group Captain Lionel Mandrake, he is holding the machine gun by the barrel. In reality, this would quickly cause serious burns and would not be possible for more than a few seconds.
In reality incoming missile threats are not detected by a radar on an aircraft as depicted in the movie, but by a Radar Warning Receiver. An RWR assesses threats by detecting a ground radar as it directs its tell-tale emissions at the aircraft to guide a missile to it, or by detecting a radar on-board the missile itself.
The depicted capabilities of the airborne radar in the B-52 are fantasy. The B-52 never had a fully rotating radar with a PPI scope, it had a ground attack radar, and the gun turret radar didn't operate like that. No airborne radar in the 1960's could detect a target as small as a surface-to-air missile at 50 miles away. A sweeping radar would not be able to display the missile exploding in mid-sweep.
When Major Kong is reading the contents of the crew's survival kits, he mentions, "one automatic pistol". The weapon shown as he reads that description aloud is a typical semi-automatic pistol, not a fully automatic weapon which continues to fire as long as the trigger is depressed - in other words, a machine gun. However, the correct military designation of the standard issue sidearm depicted is "Automatic Pistol, Caliber .45, M1911-A1."
The panel in the B-52 labeled "Auto Destruct" is in fact a flare launch control panel. Visible under the black paint are the instructions
1) PULL COVER DOWN
2) MOVE MASTER (CENTER) SWITCH DOWN
3) RELEASE A FLARE BY MOVING EITHER SIDE SWITCH"
Several times during the film, when the B52 is shown in flight from the side, even though the camera angle "pans" with the aircraft when banking (turning), there is no change in the angle or geography of the scenery on the background plate footage - it still looks as if the plane were in straight level flight.
The plane's navigation acetate we see repeatedly towards the end of the film is an rough outline projection of the whole globe. This would be completely useless for its supposed purpose of targeting a single missile base.
The first time we see the War Room, there's a binder in front of General Turgidson where the spine reads "World Targets in Megadeath". Its position changes during the long scene, and at one point we can view the contents, and the binder is empty.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
When Mandrake made the phone call to the president, the communication system was supposed to be dead. However, there are no doubt multiple phone lines going into a major air base, and it is quite conceivable that a public pay phone would be on a completely separate phone system than the direct line to SAC Headquarters. In fact, Mandrake did mention the possibility that it would not be working.
Since there has never been any real 100 MT nuclear devices detonated, stock footage of other, much smaller, devices stand in as "actors" for the 20-30 and 100 MT detonations in the film. Clearly we can forgive Stanley Kubrick for not using real 100 MT nuclear weapons to make a movie. Also, megaton explosions would not be photogenic for the rapid cuts of the end sequence since they expand much slower on film, as they are being filmed from much further away. Finally we can assume that in the early 1960s there wasn't much declassified material of megaton explosions available to the public as such explosions were achieved only less than ten years earlier.
After having shot the Coca-Cola machine, Colonel Bat Guano leans down to grab the coins and is subsequently hit in the face with a stream of the soft drink. Keenan Wynn's head was too high when the stream began to spew toward him, and he can be seen lowering his face down into it to produce the full comedic effect.