I change into (presentable) pajamas plus a sweater on top for long-haul flights--nothing goofy, just the plain dark blue jim jams that BA hands out in F. I wear compression socks and travel slippers for the flight. Bra off for the duration of the flight; fresh underwear goes on at the end. When I'm in the lav changing back into my clothes at the end of the flight, I do a little wipe-down of any body areas that may have gotten sweaty, using whatever wipes are to hand, and re-apply deodorant. I don't wear makeup, so my face just gets a little wash/wipe at the end of the flight.

That said, for almost all long-hauls I am traveling in J and get lounge (shower) access at arrivals, which I use religiously. It wakes me up and also sorts out my hair, which inevitably ends up flattened to my head after a night flight, even if it's clean.

I don't see why planes would be any dirtier than any other environment. Wash your hands and you're fine.