I presumed that the function of the microphone was so that everyone could roam about the ship. Else, just filtering out the bridge was my instant jump-to pondering point, as well. As for the ever changing conditions inside the Human body...I also presumed that even back then, they comprehended that computers would only become more complex and capable of doing a great number of things...like adjusting for variances like that. They just didn't know exactly how the tech would evolve.
Capt. Kirk: Captain's log, supplemental. Engineering Officer Scott informs, warp engines damaged, but can be made operational and re-energized.
Enterprise Computer: Computed and recorded, dear.
Capt. Kirk: Computer, you will not address me in that manner. Compute.
Enterprise Computer: Computed... dear.
Capt. Kirk: Mr. Spock, I ordered this computer and its interlinking systems repaired.
Mr. Spock: I have investigated it, Captain. To correct the fault will require an overhaul of the entire computer system and a minimum of three weeks at a starbase.
Capt. Kirk: I wouldn't mind so much if only it didn't get so... affectionate.
Mr. Spock: It also has an unfortunate tendency to giggle.
Of course, I do tend to ponder why if Finney was trying to stay hidden while enacting his revenge, he'd ever bother reprogramming the computer on how to play chess. Sure. I guess he's got to have some kind of distraction. And this ship seems rather lacking in options. But, I don't tend to think of him as being able to mentally support a whole 3-D chess board inside of his head. And, to duck into the break room sure seems like a good way to get caught.