There are so many important things to grasp when you lead a community. It difficult to pick out the most important because the one that seems the most obvious off the top of my head is "keep your mouth shut." However there are times when people want to hear the mayor speaking out. People want to be led so there are times you need to talk and make the hard decisions. After thinking it over "keeping your mouth shut" is the most important.
Most small community's have a pool of people or families who have quite a bit of influence. They may not be former elected town officials but they may have sons, daughters, cousins and in laws on the payroll. So Joe Blow might be married to Jane Doe of the powerful Doe family, and a casual remark to Joe about the Does overwhelming interference in local affairs will come back to haunt you. As you can well imagine I learned that lesson the hard way.
I have mapped out the familial relationships of the major groupings of my town carefully, but I still get surprised. I actually use the reverse system to send subtle messages back to the major players that allow me to position myself in latter discussions with them. Sometimes the direct way is not the best way.