What's bad about the jab is not Wesley's intent, but that he said it out loud in front of Kirk's subordinates. If it had been him commiserating with Kirk in private, that would be one thing, but the reaction shots on the bridge tell the story: A really unprofessional move on Wesley's part.
In the 1960s, with the draft going strong for a quarter century, a considerable percentage of the audience would find it extremely unusual for a military doctor to have attended a service academy. McCoy not being familiar with "ring knocker" terminology strikes me as more believable than it would be otherwise, really.
And, if we go by those backstories, Scotty is not an Academy man, either, having come up from the enlisted ranks and served in the merchant service. It also sounds like Chapel entered Starfleet pretty much directly from civilian life. Again, with the WW2/Cold War experience of the OS audience, a great many viewers would take for granted that there were a number of different roads to becoming an officer. It's something that has always bugged me about later Trek, that the Academy is implied to be the one and only route to a Starfleet career.
Yep, and it has been that way for ages. Military physicians are not so different from civilian that they need their own medical schools, it's much more efficient to take the products of civilian schools and adapt them to the service.