Do retrospectives at regular intervals and encourage everyone in the team to bring up (almost) any issues, large or small, in those meetings, and discuss them, with a solution-focused outlook - what can we actually try in order to address this problem?

An essential feature of retrospectives is that upper management, and internal/external customers, are not invited - and do not get to see the raw whiteboard, but only - if they see anything from it - a sanitised summary that's relevant - and diplomatic - for them. This all helps to encourage openness.