Ater watching "Court-Martial" last weekend, it occurred to me that this is a pretty good episode right up until the final act. A nice, taut, "Perry Mason-vs-Starfleet Computer" story.
I'm guessing that it was Roddenberry's edict "put the ship in danger" that accounts for the forced ending. While it was important to find Finney alive and well and hiding aboard ship, the whole subplot with him sabotaging the ship (with jumper cables) and eventually fighting Kirk is unneccessary.
I won't even go into the whole thing with McCoy's microphone and the heartbeats. Dumb.
The ending could have been improved greatly by having Kirk and Spock search for Finney...he holds them hostage with a phaser and still gets to give his impassioned speech ("Officers and gentlemen! Captains all! Except for Finney...and his one mistake!")...then Sam Cogley brings in Finney's daughter at the last moment and he cracks.
But I know Roddenberry always pushed for the "ticking clock" ending.