What legal recourse do you have if you are unhappy with a graphic designer's work?:
Depends what the contract says, I suppose.  It may call for mutual satisfaction or give you a right to ask for them to be redone.  Most likely you have to pay anyway.

However, the issue may not be best approached by means of your "legal recourse." If you haven't done so, tell the designer how unhappy you are and why, and ask that the designs be redone.  It may be that the designed will work with you to redo the work -- it would be in the designers' long-run best interests to see that his/her customers are happy with the design.