I just returned from three weeks on the Aegean and the Med, and had no issues with my K1 and airport security in any country I flew thru and to. I left in sleep mode, and it rode thru the x-ray machine in my carry-on lugage. Still works perfectly.
While on the aircraft, I had zero requests to turn it off from flight attendants. It was in its cover, so they may have thought I was reading a DTB, but still, it was really nice to keep reading while the aircraft waited on the runway for what seems like forever.
My only complaint about using the Kindle while overseas was that when I finished the first book in a series, I couldn't turn on the Whispernet and order the next book. I had other books loaded and ready to go so I was not without reading material, but I really liked this one and wanted to keep reading (I wasn't sure that I would like it which is why I didn't buy book 2 before I left). I did not take my laptop on vacation with me, so I had to wait til I got back to the US to order that second book.
I will never travel again without the Kindle! All my books in one small package in my carry-on bag!