Rental home and apartment listing site Zumper Inc. has released its first consumer mobile app that allows iPhone users to search Zumper's database and monitor the site's rentals on a neighborhood-by-neighborhood basis. The San Francisco-based site's listings, gathered from large brokers, landlords and directly from users of the free Zumper Pro landlord-focused iPhone app released in April, show up on the consumer app as a Twitter-like listings feed. Last month, Zumper took its listings site national from a beta launch in a handful of U.S. cities. Users looking for a rental in a city can select any number of neighborhoods -- the boundaries of which generated by a third-party firm -- and set up alerts for rentals that show up in those neighborhoods in the users' price range that will p...