Do you mean airshows in general, or the Airshow system used on many commerical flights to show your position, speed, etc? To record this, you'd need a video camera, and just point it at the PTV screen, or the overhead screen in the cabin. I'm not sure I understand the question exactly, doesn't seem to make a lot of sense.
Another thing you can do if the airline's version of Airshow gives your latitude/longitude co-ordinates is to write these down every now and then, and after your flight enter these figures into the Great Circle calculator at http://gc.kls2.com/
. This will show exactly what track your flight took. This is particularly interesting on transatlantic routes.