We can start with James R. Kirk.
Okay, this one doesn't show up on a personnel file (like the ones of Dehner and Mitchell) but on a tombstone created by Crazy Gary who has become rather evil at that point in WNM and is possibly showing off his wicked humor:
The first Stardate 1277.1 could just indicate the beginning of Kirk's captaincy aboard the
Enterprise ("see how short your career as starship captain has been"

) and regarding the "R" I once read that it stood for "Rice", a derogatory academy nickname (

).
Or we can start with Spock smiling in "The Cage".
Either the producers hadn't decided yet how to fine-tune the Spock character at this early stage of production and/or the half-human Spock had loosened up in his early Starfleet years (being among smiling humans) before deciding to favor Vulcan ways over human ones.
I really don't see a continuity issue here, except for the eyebrows that finally looked different.
On the contrary, the producers paid a lot of attention to continuity. Already in WNM Spock hints a female human ancestor (to become his mother) and in "The Corbomite Maneuver" states that Balok reminded him a lot of his authoritarian father - whom we saw act exactly as suggested in "Journey to Babel".
@ JarodRussell
At this point in time the erroneous turbo shaft deck numbering in ST V has not been fixed. Frankly, I think it would be better to delete this entire scene.
It's also noticable that Kirk asks Scotty for directions and not Spock. However, a few shots later, Spock remembers
exactly where to find a spare pair of rocket boots on such a short notice, suggesting he did know the layout of the lower levels of the ship.
Bob