Here I am, ladies and gents, stitching on an airplane (3-13-2011). I had my sister take this photo, blurry and silly as it is, to prove that the TSA does really let you have scissors and needles on an airplane. I can't say that it was very comfortable or that I had a lot of arm room to stitch in, but I did actually manage to finish a few hankies for custom orders.
I wouldn't recommend having your stitching out during take-off or landing since you don't want to drop your scissors or needle. The first leg of our flight was only 30 minutes, so I didn't bother to get everything out then, but the 2 1/2 hour part of the flight was much more entertaining with something constructive to do.