I recently found an elegant solution - Velcro. The seats on most airlines have a small patch of Velcro "hooks" (that's the rough side of Velcros) used for attaching a small headrest cover. In this Instructable I will show you how to mount your tablet using this small Velcro strip as a base.
Step 1: Materials
What you will need:
* 1 meter of Velcro (both sides - hooks and loops) with a sticky back
* a tablet
* cheap back cover for the tablet (optional)
Step 2: Preparing the mount
* cut a 20cm hooks piece
* cut a 20cm loops piece
* remove the protectors from the sticky back and glue these two pieces together
Now we'll need two long vertical strips. Cut two 30cm (or longer) hooks strips, and attach the tip of these strips to the sides of the base piece. Do not remove the sticky back protectors. I suggest leaving some room on the sides of the mount piece for better grip. If you do it right, you will get something that looks like a PI symbol (Π).
You'll might want to take some extra Velcro with you, for final adjustments. Just make sure you cut everything before you go on the plane - bringing scissors on board is probably a bad idea.