I've been going through my old VHS collection and paying attention to many of these things again, too.
[viewscreen lightshow] was actually kind of a production error that we got to see it in the clear in that shot.
...But in retrospect, it nicely established that what our heroes have in front of them is not a window - it's a display screen! A sudden no image -> image transition, especially if off camera, might have given a less obvious interpretation to Kirk's "Screen on" command and left the viewers confused for generations to come.
Why did he turn the power back on, anyway?
Maybe they needed to get the lifts going again, or get air circulation back online.
As we saw on Elba II, there are upsides to placing your incarceration facility in an environment that doesn't exactly cater for shirtsleeves escapes. Quite possibly, power was a life-or-death matter for Tantalus V as well.
Scotty tells Kirk and the others to bend low because "it reads pretty cramped over there." So it is - until they walk a few feet to the left where the ceiling was high enough for them.
Well, that's the location Balok specified for them... Quite possibly Scotty wasn't allowed to "read" the other spaces.
What bugs me is that the buoy is supposed to be 107 meters on a side, but it's shown as being just about the same thickness as the edge of the Enterprise's saucer, which is less than a tenth that.
This holds true if the cube is dead ahead (as suggested by the viewscreen shots). However, it's specified as being a mile away from the ship, too. Combining these two and placing the cube 1.593 meters
off to port in that fwd quarter view solves the scaling problem, then! Kirk then turns to face his opponent, giving us the view from astern, again with the cube a mile away and more or less correctly scaled. In short, a completely unintentional, extremely rare instance of dialogue matching visuals.
And similarly, the Fesarius is supposed to be a mile across but it looks much huger than that when it looms in front of the Enterprise.
Well, "must be a mile in diameter" is essentially a minimum estimate voiced by Spock after his instruments have left him without a definite mass reading. Apparently, he knows is that scale of his instrument ends at spherical ships greater than a mile in diameter. Why he fails to measure the diameter directly on some other instrument, we don't know - but a series of instrument failures is no less credible than an individual failure, and may even be a sign of Balok jamming things.
Timo Saloniemi