"Court Martial" was filmed from 3 October 1966 to 11 October 1966. The story outline and the drafts of the teleplays were written from 3 May to 26 September 1966 with a few revisions up to 3 October. It was the 15th episode to be filmed.
We see the visual computer log of the bridge. The camera seems to be positioned high above the forward viewscreen:
UHURA: Meteorology reports ion storm upcoming, Captain.
KIRK: We'll need somebody in the pod for readings.
SPOCK: Mister Finney is top of duty roster, Captain.
KIRK: Post him.
SPOCK: Attention, Commander Finney, report to pod for reading on ion plates.
FINNEY [OC]: Message Received.
SPOCK: Officer posted, Captain.
(The ship suddenly judders)
KIRK: Stand by on alert status, Mister Spock.
HANSON: Approaching ion storm, sir.
KIRK: Warp factor one, Mister Hanson.
HANSON: Warp one, sir.
(There's another sharp jerk, and Kirk presses a button on his chair panel.)
SHAW: Reverse. Stop. Go forward with magnification on the panel. Freeze that. Captain Kirk is now signalling a Yellow Alert. Go forward, normal view.
When Shaw calls for magnification on the panel, it switches to an angle filmed from behind and above Kirk. When she says to go forward, normal view, the screen shows the whole bridge from a forward viewpoint, but not necessarily the same angle as previously.
(On courtroom viewscreen.)
UHURA: Call from the pod, sir.
KIRK: Tie in.
FINNEY [OC]: Finney here, Captain. Ion readings in progress.
KIRK: Make it fast, Ben. I may have to go to Red Alert.
FINNEY [OC]: Affirmative.
KIRK: Hold our course, Mister Hanson.
HANSON: Aye, aye, sir. Natural vibrations, force two, Captain. Force three.
KIRK: Engineering, then ion pod.
UHURA: Aye, aye, sir.
CREWMAN [OC]: Engineering.
KIRK: One third more thrust.
CREWMAN [OC]: Working.
FINNEY [OC]: Ion pod.
KIRK: Stand by to get out of there, Ben.
FINNEY [OC]: Aye, aye, sir.
HANSON: Force five, sir.
KIRK: Steady as she goes, Mister Hanson.
(And the close up on the Captain's panel shows...)
And according to the transcript the computer log shows a close up from a different angle of Kirk pressing the jettison pod button prematurely, without a command from Shaw to specify the angle or the close up.
So the visual computer log seems to show the bridge from at least two different angles and with high resolution allowing for close ups when requested.
So if the computer logs of the Enterprise were sent back in time to the 20th century they could have been edited into hour long episodes. That would make everything that we see and hear in Star Trek episodes accurate.
"The Menagerie, Part I" and "The Menagerie< Part II" were written from 12 August 1966 to 10 October 1966, with revisions up to 17 October. They were the 16th episode filmed, from 11 to 17 October 1966. Repeat, "The Menagerie" was filmed right after "Court Martial", so there was little time for the production staff to forget details of the plot of "Court Martial".
In his court martial, Spock shows images of events thirteen years ago on the Enterprise and on Talos IV.
MENDEZ: Why? What does it accomplish to go there or to take Captain Pike there? I want to know why.
SPOCK: Are your comments a part of the record, sir?
MENDEZ: Yes, it's on the record.
SPOCK: Thank you. Request monitor screen be engaged.
MENDEZ: For what purpose?
SPOCK: To comply with the request you just made, sir, that I explain the importance of going to Talos Four.
KIRK: By asking why, you've opened the door to any evidence he may wish to present. Apparently what he had in mind.
MENDEZ: Present your evidence. Screen on.
SPOCK: This is thirteen years ago. The Enterprise and its commander, Captain Christopher Pike.
As I remember the screen shows the opening scene of "The Cage" with the camera zooming in on the bridge dome and passing thorugh it to show the bridge from overhead. When Spock speaks the camera angle shifts to a normal height from the overhead view, I think.
SPOCK [on screen]: Definitely something out there, Captain, headed this way.
KIRK: Screen off. Chris, was that really you on the screen? (flash) That's impossible. Mister Spock, no vessel makes record tapes in that detail, that perfect. What were we watching?
SPOCK: I cannot tell you at this time, sir.
MENDEZ: Captain Pike, were any record tapes of this nature made during your voyage? (flash, flash) The court is not obliged to view evidence without knowing its source.
SPOCK: Unless the court asks a prisoner why, Commodore. You did ask that question.
They resume watching the scene on the bridge. Then Pike goes to his quarters and Dr. Boyce visits him and they talk. It seems to me that would have been a good time for Kirk to say no ship makes record tapes that good, because respect for privacy would probably keep the computers from recording in a person's private quarters.
Or Kirk could have said that starships just recently started making record tapes in that detail, that perfect, instead of saying that they don't. He could have asked Pike if possibly there was an earlier experimental system to do so at the time of the Voyage to Talos IV, and his words suggest that he did, but Kirk failed to make it clear that ships do so now but just recently started, and changing a few words would have made that clear.
no vessel makes record tapes in that detail, that perfect
means that no recordings on the bridge are as detailed as seen in "The Cage", even though the bridge is the part of the ship likely to have the best automatic visual and sound recordings, then no scene in TOS can ever be an edited version of computer logs sent back in time to the 20th century.
At the best, written accounts of events on the Enterprise could be sent back in time and used as the basis for scripts to film episodes using actors holding props and wearing costumes in sets. Then the characters would not really look or sound exactly like the actors, and the costumes, props, and sets could only approximate the look of the originals, if the information sent back in time to the 20th century even included visual details.
So "Court Martial" and "Menagerie" give greatly conflicting information about how detailed visual computer logs are, and thus of how faithfully TOS episodes reproduced the look and sound of the "actual" future events.
So how do we reconcile the two episodes?
One method would be finding the order of the two episodes.
The story outline for "Court Martial is dated 3 May and revised 26 June 1966. The first draft script for "Court Martial" is 15 July and the first draft for "Menagerie" is 12 August. The second draft for "Court Martial" is 6 September and for "Menagerie" is 3 October. Final draft for "Court Martial" is 26 September and 7 October for "Menagerie".
"Court Martial" was filmed from 3 October to 11 October and "Menagerie" was filmed from 11 October to 18 October.
So "Court Martial" has been made earlier than "Menagerie" all the way so far. But after filming came post production with optical and sound effects added and editing. I don't know when or in which order the episodes were completed and delivered to NBC.
The three most popular orders to view Star Trek episodes and/or to imagine that they happen in are:
1) production order, which puts "Court Martial" immediately before "Menagerie".
2) stardate order, in which "Court Martial" at stardate 2947.3 is followed by "Menagerie, Part I" at stardate 3012.4, with no intermediate episodes.
3) Broadcast or air date order, which puts "Menagerie" aired on 17 and 24 November 1966 ahead of "Court Martial" aired 2 February 1967, with seven episodes aired in between.
If "Court Martial" happens before "Menagerie" in both production and stardate orders, possibly enough time passed between the two episodes for Starfleet to stop making as detailed visual logs as it did in "Court Martial". Perhaps only a few starships and other Starfleet vessels were selected to experimentally make such detailed tapes, and many crew members complained about feeling watched or else acted unnaturally hoping to make good impressions on whoever watched the tapes in the future, and maybe Finney manipulating the tapes to frame Kirk was the last straw and Starfleet ordered all ships to stop making visual computer logs sometime before "Menagerie".
By the time of Star Trek II: The Wrath of Khan Starfleet resumed making visual computer logs, at least in the engine room during emergencies, as seen in Star Trek III: The Search For Spock.
On the other hand, if "Menagerie" happened sometime before "Court Martial" as in their air date order, then perhaps Starfleet was inspired by the events in "Menagerie" to order the use of visual computer logs, and the Enterprise might have started doing so a short time before "Court Martial".
Presumably that would have continued until the time of Star Trek II: The Wrath of Khan as seen in Star Trek III: The Search For Spock.
And in either case the 90 or 100 years between TOS, TNG, DS9, and VOY gave plenty of time for the use of visual computer logs to possibly be started and discontinued and resumed a few times, so the practices in one era of Star Trek do not necessarily provide much evidence about the practices in other eras.