Re: So Cadet to Captain in what... a week?!
In all the scenes with black shirted Kirk and Spock hating/hitting him, Kirk has that injury under his eye - on the shot of him on the bridge in a captains shirt and giving Spock a friendly backslap, his hair is subtly different and his injuries are gone. Odds are that scene does not follow on in any quick succession from the 'black shirt' scenes.
Also, in the latter shot, Kirk is wearing the stripes of a full Captain.
Which would be why cultcross
described it as "a captains shirt", presumably.
(And it's McCoy on the receiving end of the slap on the shoulder, I believe.
Dinosaurs are just really, really big chickens.