For state - Transfer of a firearm to an unlicensed person (lacking common carrier status, the clerk lacks the ability to possess prohibited items and not be in possession)
Federally - Acting as a dealer or gunsmith accepting a gun and arranging service for it. You cannot legally take your friends gun, service it, and then have a third party ship it back to him unless you are fed licensed gunsmith (and even then, you have to do the return/transfer on your books). Once again, the lack of common carrier status is the issue.
Company policy - UPS has a policy for EVERYTHING. Even which way the teeth on keys are to point when approaching the package car and which foot goes on the step first. I would expect a "no guns at UPS store" policy, but have not confirmed this.