Alex Kozinski, chief judge of the U.S. 9th Circuit Court of Appeals, has been Gangnam styled.
Is this legal?
Maybe, and this is just the type of question you might expect as counsel for JibJab. The video raises more than just questions regarding rights of publicity. Specifically, do the folks over at JibJab have a license to allow users to make derivative works of the original video? Can they allow users to create videos, knowing the videos will likely be distributed far and wide? If you create your own video on JibJab's site and exceed the scope of any permission the Gangnam Style folks gave, can JibJab be held liable for its customers' actions? Does parody fit in to a legal analysis in this case? Does it matter that JibJab has faced litigation before? Who owns the copyright in the Kozinski video---JibJab, the professor who created it, the person that owns rights in the photo of Judge Kozinski, Judge Kozinski?
Check out Music Copyright Law; Intellectual Property Rights in Sound Recordings, Film & Video; or Kohn on Music Licensing for answers.