(at home or at the office or in the airplane) Toilet paper is extremely effective in sopping up wetness that even the quicker picker upper paper towels won't snag. Next time just go to the plane lav and get some. Also next time you spill something on the carpet or sofa, give it a try. You'll need to squeeze hard.
(Philosophical) If you were able to detach the seat cusion and turn it upside down, would it be dry on that side?
Cleaning tips:
http://members.aol.com/ajaynejr/clean.htm