I looked under my Snapple cap today and there read Snapple Fact #147:
Panama is the only place in the world where you can see the sun rise on the Pacific and set on the Atlantic.This makes absolutely no sense. I can't conceive any possible way in which the sun could rise in the west and set in the east, no matter where you're standing in Panama or Chile or anywhere.
Update: Dr. Weevil explains in comments: "Check the map: Panama is twisted, so part of the Pacific coast faces east, and part of the Atlantic coast faces west. I doubt there's one single point in Panama where you can see the sun rise from the Pacific and set in the Atlantic, but there should be points where you can see one or the other." Like KT Tunstall, suddenly I see.