If you'd like to start a new thread I won't object, but you might need to explicitly point me to it. 
This may not be a great example, especially since I think Kirk was rather deliberately giving off attitude at the time, but when we see Kirk taking the KM scenario he's being highly belligerent. Really, how much more disrespectful can you get than obnoxiously eating an apple while sitting in the center seat and scolding your communications officer for not saying "Sir"? Granted Uhura erred there, but Kirk's retort was hardly professional either. He also not only renders the Klingon ships helpless but proceeds to blow them out of the stars. Satisfying for his fellow test-takers perhaps, and granted we don't know the status of relations with the Klingons at this point, but gunning down helpless ships doesn't exactly seem to reflect Starfleet ideals. He could have hailed them, could have ignored them, etc...especially given that he programmed the alterations to the test. It's entirely possible that PrimeKirk handled his third round of the simulator the same way...but I doubt it.
At the end of the film Nero's ship is in much of a similar situation to the Klingon ships in the KM scenario, but Kirk reaches out, even considering that doing so could lead to stronger relations with the Romulan empire (and maybe in the end heal Nero's psychological trauma to some degree). The ship itself needs to be destroyed so as to eliminate any possibility of further disruption to the timeline (arguments as to whether this is in fact Kirk's reasoning notwithstanding), but there's no reason to kill the crew with it.
In any event, Kirk goes somewhat (granted not tremendously, but he's under a bit of a time crunch and probably not very favorably disposed towards Nero) out of his way to offer Nero assistance, and it's the logical, pacifistic Spock who disagrees and says Kirk should kill the Romulans in cold blood.
I won't deny that this is not the strongest of examples, but it does illustrate Kirk facing a similar situation - a helpless enemy vessel - and showing some character growth.
Other possible examples-
Proceeding the mind-meld, Kirk may not exactly -like- Spock, but no longer seems as inclined to antagonize him on general principle. I don't think he took any particular joy from proving that Spock was emotionally compromised...and that's before he got thrown over the helm. It's safe to assume they aren't friends by the end of the film either, but Kirk's learned to respect the guy at least. No matter what Old Spock told Kirk, I don't think Kirk would have bought into it if Young Spock hadn't shown some growth himself.
While Kirk clearly gets off to a rocky start with Uhura, he seems to have moderated his antagonism towards her as well by the end of the film.
I haven't looked at the film specifically for this, but it may be a valid argument that by the end Kirk seems more willing to form plans with others' input and feedback, rather than acting on his own initiative and without asking for (or listening to) what others have to say.
This may not be a great example, especially since I think Kirk was rather deliberately giving off attitude at the time, but when we see Kirk taking the KM scenario he's being highly belligerent. Really, how much more disrespectful can you get than obnoxiously eating an apple while sitting in the center seat and scolding your communications officer for not saying "Sir"? Granted Uhura erred there, but Kirk's retort was hardly professional either. He also not only renders the Klingon ships helpless but proceeds to blow them out of the stars. Satisfying for his fellow test-takers perhaps, and granted we don't know the status of relations with the Klingons at this point, but gunning down helpless ships doesn't exactly seem to reflect Starfleet ideals. He could have hailed them, could have ignored them, etc...especially given that he programmed the alterations to the test. It's entirely possible that PrimeKirk handled his third round of the simulator the same way...but I doubt it.
At the end of the film Nero's ship is in much of a similar situation to the Klingon ships in the KM scenario, but Kirk reaches out, even considering that doing so could lead to stronger relations with the Romulan empire (and maybe in the end heal Nero's psychological trauma to some degree). The ship itself needs to be destroyed so as to eliminate any possibility of further disruption to the timeline (arguments as to whether this is in fact Kirk's reasoning notwithstanding), but there's no reason to kill the crew with it.
In any event, Kirk goes somewhat (granted not tremendously, but he's under a bit of a time crunch and probably not very favorably disposed towards Nero) out of his way to offer Nero assistance, and it's the logical, pacifistic Spock who disagrees and says Kirk should kill the Romulans in cold blood.
I won't deny that this is not the strongest of examples, but it does illustrate Kirk facing a similar situation - a helpless enemy vessel - and showing some character growth.
Other possible examples-
Proceeding the mind-meld, Kirk may not exactly -like- Spock, but no longer seems as inclined to antagonize him on general principle. I don't think he took any particular joy from proving that Spock was emotionally compromised...and that's before he got thrown over the helm. It's safe to assume they aren't friends by the end of the film either, but Kirk's learned to respect the guy at least. No matter what Old Spock told Kirk, I don't think Kirk would have bought into it if Young Spock hadn't shown some growth himself.
While Kirk clearly gets off to a rocky start with Uhura, he seems to have moderated his antagonism towards her as well by the end of the film.
I haven't looked at the film specifically for this, but it may be a valid argument that by the end Kirk seems more willing to form plans with others' input and feedback, rather than acting on his own initiative and without asking for (or listening to) what others have to say.
