any ideas for finding out if a competitor has received authorization from the regulators to open a branch bank?

Look in the newspaper classifieds and various banking periodicals for your region. That is a "local" solution. I'm not sure if it is available on the regulator's Web sites or not.

Let me append my last reply. Go to the regulators Web sites and do a search on the bank's name, assuming you know it. I did that at the OCC site and the first hit was my CRA PE, the next was the notice they publish of requests, (expansions, withdrawn, approved...) which included some of ours.