When Rufus poses as a janitor in the control room he empties out the same ashtray twice.
Burl's mistake in the tape mount has been reported over and over (it was on the correct [right] side, but the reel was backwards, face-in), but he also manually shoved the tape drive door up to close it. The door operated automatically when the mount sequence was started by pressing the button on the panel above the drive door.
When Anthony Bruhl changes out the mag tape in the IBM 729 tape drive, he puts the reel on backwards. The "no write" ring is facing outwards. This ring must be facing inward for the machine to operate.
In an early scene at Mission Control, the image of John Glenn in his Friendship 7 fight is shown on the big screen.
When Bruhl is impersonating Ellis, he goes into the computer room and mounts a magnetic tape on a tape drive to load some data. When he has the tape in the briefcase the backside of the reel shows a yellow write ring in place. This is on the back side of the mag tape reel. When he mounts the tape onto the drive the yellow write ring is facing forward, which means the tape was mounted backwards.
When Bruhl mounts the magnetic tape reel onto the tape drive in the computer room, he puts it on backwards. The yellow ring is supposed to be on the inside. It is a write enable ring. When in place, it allows the tape to be written to. When removed, the tape can only be read from.
Lucy says that if Apollo 11 fails the Soviets will be energized for the space race and the US could potentially lose the Cold War. She correctly mentions that they are close to completing a program of automated return of lunar rocks by unmanned craft.
This was achieved by Luna 16 in September 1970, after the failure of earlier missions planned to be ahead of the US landing. It got little attention - but things would have been otherwise if Apollo 11 had failed. Historically, Apollo 12 was also ahead of Luna 16. But it is most unlikely it would have happened had Apollo 11 failed for unknown causes.
The Soviet system was also still strong in the 1970s. Many expected, feared or hoped that they would win the Cold War.
This was achieved by Luna 16 in September 1970, after the failure of earlier missions planned to be ahead of the US landing. It got little attention - but things would have been otherwise if Apollo 11 had failed. Historically, Apollo 12 was also ahead of Luna 16. But it is most unlikely it would have happened had Apollo 11 failed for unknown causes.
The Soviet system was also still strong in the 1970s. Many expected, feared or hoped that they would win the Cold War.
In the middle of the live TV broadcast of Neil Armstrong stepping on the lunar surface and making his "That's one small step for man..." announcement, the image switches from a side view of the ladder, from the exterior of the Lunar Module, to an overhead view of Armstrong from the interior of the Module. The exterior camera was the only available live TV feed. The overhead view was shot using a film camera and the film, which was a much higher resolution than that of the TV camera, was not developed or shown until after Apollo 11 returned to Earth.
The "virus" shown on the screen is not only not source code from anything, it's from an MS-DOS based system, which would not exist for another 12 years. NASA created and used a proprietary operating system called HASP.
Wall sized display screens in use in 1969 were one-off, analog systems and did not have firmware to display things like "NO SIGNAL" when the signal is cut.
The keyboard in the NASA computer room is of modern design. Keyboards in 1969 were much bulkier.
When creating the fake ID they are using an X-acto knife with a self-healing mat. The mats weren't invented until 1979 by Olfa for use with rotary cutters.
When the computers get hacked, Mission Control's video projectors switch to color bar test signals. However, these are the three-row SMPTE color bars introduced in 1978 rather than the two-row color bars in use in 1969.
Apollo 11 was on July 16, 1969 in Houston Texas and it was 84.9 degrees F. During the outdoor scenes everyone is wearing over coats and jackets.
The series has made it abundantly clear that the time travelers may never visit an era in which one of their previous selves was then living. However, in 1969, the character of Anthony Bruhl would have been 10 or 11 (actor Matt Frewer, who plays Bruhl, was born in 1958).
In this episode they travel back to 1969. With the premise being that no one can travel back to a time within their own lifetime then that would mean that the character of Anthony could be no older than his late 40s. This is a bit of a stretch since Matt Frewer was 60 years old at the time.