Existent initiatives such as simulation, leadership walkarounds, near miss reporting, failure identification & analysis, and disclosure programs come to mind, but I am open to hearing about others.
Culture of safety is measurable using "Culture of Safety" survey instruments. In my view, one of the most valuable tools is front-line provider input that is cross-disciplinary (eg, physicians seeking input from nurses on where patients might experience preventable harm).
Daniel -- you are so right that cross-disciplinary discussion can tease out tacit knowledge. Thanks for sharing this example.
You may find our paper "Working Together for a Collective Culture of Construction Safety" (hosted on RG) provides an interesting initiative and a useful analogy to safety in the medical field. We looked at the stakeholders and discovered that many were not documented in the literature. You may like to draw your own Fig 1. for the medical field.
Tacit knowledge is highly correlated with intuition and this could be linked faith/belief, so an initiative that value the belief and cultural practices of the community in place will work