For Boating citations, probably not. except that a warrant for arrest in Arizona will be issued, which winds up costing about 3 times as much in additional fines, not to mention the hassles of being arrested, poting bail, etc. if you're caught in Arizona.
For traffic cites, you're driving privileges in Arizona will be suspended. Some states MAY suspend your license if you have a ticket outstanding in Arizona. Also if it's a "Criminal traffic cite, a warrant will be issued, as above.
In both situations the court will treat the outstanding tickets as a "debt", and bring in a collection agency to collect the debt, putting a ding on your credit record.