I'll agree with Can, winning a one on one dogfight without resorting to missile spam is a proper skill. For combat, I would add the destruction of enemy ground defenses, particularly Udlaoy destroyers, as something that takes practice and talent to perfect. Dodging missiles without flares is particularly advanced, but rather difficult to precisely track.
For skills that are relatively easy to learn, but challenging to master, carpet bombing, missile armed interception - particularly when missiles are used sparingly, and I'd most likely put carrier landings in here as well.
Moving on, I'm a touch outside my comfort zone, but I have some suggestions which others could improve upon.
For civilians, I'd say really proper precision landings, particularly under the direction of ATC, would be a particularly noteworthy skill. For airliners, flying a proper route as close as possible to certain recommended parameters, such as speed, altitude, bank angle, g-loading, and total time, would be an excellent challenge.
For acro folks, I would include the correct performance of recognized maneuvers would be worth something. Really top notch formation flying could go here. It would be appropriate to make some sort of note of air show performances, particularly when they are well executed.
[CAG171]Bombcat, Commander, Air Wing 171
Team Awesome # 23