How do you deal with unfavorable responses to new public art?

There is no public art commission that will please every member of the public, and most public art programs will face some unfavorable responses to new installations in the course of their work. It is important to listen to all feedback, and if there is a reasonable manner of addressing the complaint, an organization should consider doing so. It is also important to remember that many installations initially face negative reactions, but that opinions can and do change over time.  
The artist Garth Evans has argued that some people will disagree with any changes to their local environment, be that a new trash can, advertisement, or artwork. (Garth Evans and Jon Wood, The Cardiff Tapes (1972) [Chicago: Soberscove Press, 2015], 83.)
Inclusive, transparent, and thoughtful commissioning processes, and efforts to educate the public about new installations, can help head off potential conflicts before they happen. But when conflicts do occur, be sure to listen, exercise patience, document the complaint, and be prepared to respond. If your local government has processes for addressing complaints, familiarize yourself with them.  And remember, art is often designed to provoke a reaction, and sometimes that reaction is negative no matter the best intentions of the artist or commissioning organization.