The extent of the Estate's rights is a tangled skein. They clearly think, for instance, that they retain enough rights to block the Lord of the Rings museum in New Zealand housing props, costumes, and miniatures from the movies. I'm not sure whether this matter has been resolved yet or not.
This past summer, the Estate apparently also contacted a site called
http://www.shiremail.com, claiming that
they own the rights to the word "Shire", which may be taking things a little far...