I started my practice of Agile coaching by bringing a notebook (one per team) to all team events. I jotted down anything that I otherwise might have spoken up about. The first thing I learned was that things I noted normally got fixed without me saying a word, minutes or days later. They sometimes evaporated into non-issues. Other times, the team noticed the issue and self-corrected. Had I spoken up instead of taking a note, I would have either made an issue out of nothing, or I would have taken away from the team the chance to solve it themselves. Worse, I would have reinforced my position as unnecessary intermediary.
Writing things down allowed me to relax in the knowledge that the observation would not be lost, but also allowed me to look back and see which problems I was wise not to pounce on.