The age difference is actually more or less explained for everyone. McCoy is a significantly older recruit for whom Star Fleet is a second career. Kirk doesn't appear to be as old as McCoy, but he screwed around for some time before joining up, and his youth as a captain can be attributed to being the greatest thing since sliced bread. Scotty had enough of a "career" in Star Fleet for him to be a bit older (although the actor doesn't look old enough). Chekov is exactly 17, so he could easily be 15-20 years younger than McCoy and 10 younger than Kirk/Scotty. Sulu is the hardest, since he doesn't look as young as Chekov. In fact he looks just about Kirk's age, but we get no back story for him, so it's possible he was a bit older when he enlisted.
Generally, on the list of plot holes, I would put their age differences toward the bottom, way behind the weak plot behind the crisis driving the movie, "Red Matter", and Kirk and old-Spock finding each other randomly on a frozen moon. (In fact, the little thing that really bugged me was that the second "monster" on that moon continued to pursue Kirk instead of eating the significantly larger mammal that had been pursuing Kirk.)