Captain Christopher is seated in his jet fighter. When he is beamed on board, he is standing instead of being still in a seated position.
Roger Perry's character is consistently referred to as Captain Christopher and wears the insignia of an Air Force Captain on his uniform. But the credits list him as "Major Christopher."
When the F-104s are initially scrambled, the 2 aircraft shown taxiing from revetments are armed with AIM-9 missiles on the wingtip stations, however the aircraft shown taking off is clean.
Kirk orders the transporter room to beam up Captain Christopher as an emergency because his plane is breaking up. However, Kirk makes it to the transporter room before Christopher has even fully materialized. The transporter room has always been a good distance from the bridge, as seen in Let That Be Your Last Battlefield (1969); there is no way Kirk could have made it there that quickly. It's possible that Kirk could have used the same trick as he did in Wolf in the Fold (1967) and held Christopher in "stasis" in the transporter beam, but he gave no such order to the transporter crew.
As Captain Christopher is approaching the Enterprise, the chin strap is alternately fastened and hanging free.
In the original (not remastered) version, the Enterprise leaves Earth orbit and slingshots around the Sun to achieve time warp. However, the shots of the Enterprise exterior shows the ship passing several other stars as it moves through space. There are no stars between the Earth and the Sun.
Captain Christopher is assigned to Air Defense Command, and clearly shows an ADC qualification level insignia on the left sleeve of his flight suit. However, the stock footage of F-104's used on screen shows aircraft with markings from Tactical Air Command. Also, Christopher's flight suit is an over water suit, and he intercepted the Enterprise over Nebraska. The actor's costume should have been a sage green K-2B flight suit, reflective of location and mission.
Air force security wore their berets with the flash (patch) almost, if not all the way, over their ear when it should have been over their left eye.
During the slingshot attempt around the Sun, the speeds the characters talk about are impossibly fast. For example, if the Enterprise were traveling at warp 8 between the Sun and the Earth, it would overshoot the Earth by millions of miles within minutes, yet the elapsed time between the Sun and the Earth is clearly about the speed of light even though the ship is supposedly traveling much faster.
The SSgt Security Policeman that catches Kirk and Sulu is wearing Distinguished Flying Cross and Air Medal ribbons - He has no aeronautical wings which would indicate he isn't (and hasn't) been on flying status. It is doubtful a person not on flying status would have received these awards.
When the pilot is beamed aboard, Spock calls the transporter room to ask Kirk if he wants the tractor beam turned off. After the pilot's plane disintegrated, it would be totally unnecessary to leave the tractor beam activated. Spock would know that the next logical procedure is to turn it off, but Spock might be concerned about falling debris and thus asks for orders.
The Air Force Air Police are armed with unusual grips on their duty weapons. The guards are wearing the Air Police Shield and dressed as SAC Elite Guards. Unique to the guard, was a distinctive blue beret with the SAC crest and a bone handled, chrome plated, Smith and Wesson .38 caliber revolver in a cross draw holster.
The Enterprise is shown traveling across the sky in earth's atmosphere. The Enterprise would not be able to do this since it does not have the aerodynamic ability to fly through the air as an aircraft would do.
In the first scene on the Enterprise bridge, the "computer screens" above Uhura's station are clearly made of paper; the paper screen is not pulled tight, and there are obvious folds in it.
When the Air Sergeant is holding the equipment belts, both of the communicator props are seen with their cover/antennae hanging open. Since this activates the unit, the Enterprise would have heard everything. Additionally, when the communicator beep is heard, both units are still on the belts. In the next shot, he is holding one in his hand.
When the Enterprise is clearly in Earth's troposphere (the heaviest, densest atmospheric layer), it's said to be in orbit. Orbital speed is 4.7 miles per second, or 7.5 kilometers per second.
The Enterprise is shown orbiting 1960s Earth. If you look at the shot of Earth, the continents appear to be reversed.
F-104 Starfighters like the one piloted by Captain Christopher were never stationed in Nebraska. Had the "Omaha location" needed to scramble fighters, they would have been F-102s from Grandview Air Force Base in Missouri.
When Kirk and Sulu are prowling the base in Nebraska, the door to the computer center reads, "498th Airbase Group." There is no record of such a command in the United States Air Force in 1967. The closest would be the 498th Nuclear Systems Wing, which was stationed at Kirkland AFB in Albuquerque, New Mexico. This unit was deactivated in 2012.
Captain Christopher states that he "turned on my wing cameras. I got close enough to take some pretty clear pictures of you. Air Defense Command will be processing that film fast." And indeed Kirk and Sulu transport down to the airbase to try to retrieve the film. But since according to Spock the aircraft completely broke up, the film and wing cameras would have fallen to the Earth as debris, and recovery of the film would surely have taken a long time, as it would have required a massive search over a large area, if its recovery was possible at all.
Spock states that Captain Christopher's disappearance would not make a significant difference because he's made no historically relevant contribution. A person doesn't have to be historic for his disappearance to change history. As a USAF pilot, his going missing would generate nationwide media attention. Among the countless scenarios of what could happen, most importantly his family would be affected the most.
The crew of the Enterprise discovers an easily repeatable maneuver to accurately travel both backward and forward in time. If this were truly the case, then time travel wouldn't be as risky and unusual as it is repeatedly shown to be in the Trek Universe.
The Air Force security offices who discover Kirk and Sulu are all wearing side arms, however, while they have plenty of opportunity to draw their weapons they choose the fight in hand-to-hand combat.
There are security alarms for the photo lab but not the Statistical Service Section.
Just after Kirk orders Uhura to contact Starfleet and inform them of the black star, he walks over to talk with Spock. Just behind Spock's right shoulder (left side of screen), the shadow of a boom mic can be seen above the status displays.
Spock and Dr. McCoy are in the transporter room, when Kirk and Sulu are on the surface. A large boom mic shadow appears directly next to Spock's head, well inside the frame. The shadow then visibly moves up and out of the frame.
In Requiem for Methuselah (1969), Spock, during a mind meld, can order someone to "forget". It is unclear why he didn't meld with Captain Christopher for this purpose.
Captain Kirk introduces Mr. Spock to Capt. Christopher as "Lieutenant Commander Spock". Spock's rank throughout the entire series is Commander, not a mere Lieutenant Commander. Here, he is wearing the rank insignia of Commander (two full bars).
In the discussion of the 'slingshot' around the Sun, Spock refers to seeking out the Sun's 'magnetic attraction'. The magnetic force, while much stronger than gravity, is only effective over a short range, and it is actually the gravitational force of the Sun that is used.
When Captain Kirk and Major Christopher first get into the turbo lift to go to the bridge, the Captain states that the Enterprise is in this time period by mistake and Major Christopher says, "You seem to be having a lot of those" This is the first admission of an error by the Enterprise, there is no way that Christopher could know of any other mistakes. However, he could have been referring to hearing that his plane broke up with Kirk's admission "I didn't know your craft couldn't stand up to our tractor beam."
When Kirk jokes with the Air Force colonel that he is "a little green man from Alpha Centauri", he mispronounces the last word as 'centu'ry', with the stress on the second syllable.