Do I hear Samuel L Jackson asking about this? SHORTS, ON A....
Only issue with wearing shorts on a plane is that you might get cold. It does happen.
Yes, on some flights, they keep the cabin temps cranked up too high (this is common on Asian airlines). I've experienced that more than a few times.
I've also been on flights where the cabin temps were frigid. On my last flight to Mexico (ironically, on Alaska Airlines) the cabin was absolutely freezing. An hour into the flight I was literally shivering in my seat and had to dig a fleece jacket out of my carry-on (and I'm built for cold, northern climates, so if I was shivering, it was really cold).
Additionally: If you are seated next to/near a door or emergency exit row, the seats nearby can be quite a bit colder than other seats just a row or two away. Makes you realize the air temperature outside is well below freezing at high altitudes!
Bottom line: There are no issues regarding shorts as appropriate (from a fashion standpoint). But for your own comfort, be sure you have at least a thin jacket or other warm layer in your carry on in case you get cold (because you might).