What do you do to recover quickly from early missteps in a new role? How can you keep initial mistakes from coloring perceptions when you’re still trying to establish your reputation at a new organization?

Be patient with yourself. It takes time to (re)build trust, but if your intentions and communications are aligned with your team's, they'll be noticed and you'll bounce back. 

My strategy:
Open initially a discussion with every stakeholder about expectations in both directions and adopt to this. Establish a communication on regular basis with the appropriate frequency. Take notes on the results.

One way I do is that recalling that mistake and telling how I improved in appropriate forums and informal chats. Example: Oh my! Can't forget how I missed that particular aspect when I first rolled out the MFA police last week. How silly it was for me to miss that aspect. Now all set and we are doing great.