I am unable to sync purchased tv shows from my MacBook pro to my iPhone 4.
Instead I get an error:
(show name) was not synced to "My iPhone" because you are not
authorized for it on this computer
This seems to be the same problem- but with a movie
https://discussions.apple.com/message/16794815#16794815
Best Answer
In the "Store" menu in iTunes, choose "Authorize this computer..." then enter the credentials for the iTunes account you used to buy the movie.
If you have done this and still get this error message, then something in that file or your iTunes account is broken. In this case, you will need to contact iTunes support: http://www.apple.com/support/itunes/contact/
I hope this helps.