You run into problems with infringement with all of your additional proposed uses of copyrighted material, stiffkick80.
You would need a license to show your "The Simpsons" DVDs in your restaurant (whether your purpose is for actual viewing of the episodes or for ambience), and everything you see that has been created on a tv show or in a movie would be protected from unauthorized use by others, as well (ie. the Duff beer sign).
Copyright holders own the rights to any original and creative works that they have expressed in tangible form (on paper, audio, visual, computer disc, canvas, etc). The rights they have are the
exclusive right to reproduce their works, display or perform their work, distribute their work, and prepare adaptations (derivatives) of their work.
To use copyrighted material in the manner you propose in your second post, you need to acquire permission from the copyright holder. You can contact the holder of the rights to inquire about getting a license to use their material for your restaurant (although a license to use "The Simpsons" would, no doubt, be expensive).
The major difference between your first proposed uses and your second proposed uses is that, in your first uses, you are merely displaying property you have legally purchased already and you are not using them in a commercial manner nor are you implying with your uses any endorsement by or connection with the owner of the rights. You are also not reproducing the legally purchased items or offering reproductions for sale. The uses you are proposing in your first post would be covered by the Copyright Act's "first sale doctrine" which allows for the purchaser of any legal copy of a copyrighted work the right to do with their copy whatever they want,
as long as the use does not infringe on any rights of the copyright (or trademark) holder.
With the second set of uses, you would be reproducing copyrighted (and trademarked) material without permission from the holder of the rights, and you would be displaying, and potentially profitting off the showing of, protected material, when you run your DVDs for viewing by the public. Showing "The Simpsons" in your restaurant could be seen as a draw to your restaurant, increasing your bottom line, whether you charge for the viewing or not. In addition, the DVD pack, as cyjeff noted, has warnings about public uses of the DVDs. When you purchased your DVD set, it clearly notes that the DVDs are for
personal use only. Among the rights a copyright holder has (under 17 USC Section 101) is the exclusive right to
publicly perform or display their work. Under this provision of the Copyright Act, the right includes the performance or display of a copyrighted work "at a place open to the public or at any place where a substantial number of persons outside of a normal circle of a family and its social acquaintances is gathered."
So, you would be (generally) safe from suit on your first set of ideas for your restaurant, but you could easily be sued over your second set of ideas for your restaurant, should you implement those plans without obtaining prior permission and a license for use. "Generally safe," by the way, means that anyone can sue anyone else for pretty much any reason at all, whether a suit has merit or not.
For additional information on the copyright law, you can go to the Copyright Office's official website at
http://www.copyright.gov and for additional information on trademark law, you can go to
http://www.uspto.gov.
