The final obstacle course, were Zack abandons the chance of breaking the record to go back and yell encouragement to Casey until she finally manages to climb the rope-climb wall.
When all of the newly commissioned naval ensigns are lining up to get their first salute from their former Sergeant Instructor, and Foley's salute of Seegar begins before she's even on the platform in front of him, acknowledging the fact that he's proud that she made it when no one thought she could.
That whole scene deserves some further elaboration: it is naval tradition for new ensigns to give a silver dollar to their drill instructor for their first salute, and also a tradition for that drill instructor, when given a silver dollar from someone they felt was an exceptional cadet, to place that dollar in their right pocket instead of their left. Mayo's silver goes into Foley's right pocket.
The ending, just the ending. Even a cynical anti-romantic like me melted when Zack came for Paula and carried her out of the factory to Up Where We Belong.
Years after the movie was made, the Director was being interviewed and the ending was brought up, with an observation that some people thought the ending was a little corny. The Director replied that anyone who thought that entirely missed the point of exactly who was rescuing who. Double Heartwarming.
Near the end of his Training from Hell, Zack is forced to do some exercises with Foley near the ocean. After the instructor finally begins to let up, Paula, Syd, and Lynette drive past past the spot on their boat, mooning Foley and shouting words of encouragement to Zack. This is something in itself, but the following exchange really cements it.