Corrected entry: When McCoy is working on putting Spock's Brain back it is obvious that his arms are too high up to be doing anything other than fiddling about with Mr Nimoys forehead. (00:42:20)
Corrected entry: When they arrived in the system they said they were heading for the sixth planet in the system of Sigma Draconis, but in his captain's log about halfway through the episode, Kirk calls it Sigma Draconis VII.
Correction: Sigma Draconis VI and VII may have orbits that intersect twice, so that, when first discovered and named, SD VII was seventh from the sun, but on this visit, it is 'currently' the sixth. (See "The Wrath of Khan" for the Ceti Alpha V & VI mis-recognition issue for a similar, not identical, situation.)
Correction: Of course, the good Doctor would not be fiddling with Spock's forehead using his hands. He'd be manipulating mechanical servos (Waldos) or something analogous, since reconnecting neurons would require microscopic instruments and likely nanotechnology.