A recent article in the Harvard Business Review (see below) points out that teams that share personal insights with one another are higher performing than teams who don't. This is both because team members are better able to read each other's intent the better they know each other, and also because it brings to the fore the different strengths of the different members of the team.
One of the hallmarks of dysfunctional teams is that they do not recognize the resources that all of the different team members bring to the table. Not recognizing that means that the team isn't able to leverage those strengths. This dynamic is hugely important for boards of directors. A great board understands the different things that each member of the board can bring to the table. The best way for all board members to determine this is for the directors to spend some unstructured time with each other. A lunch before the meeting or dinner afterwards, for example.
It may seem impossible to carve out that much time, but great boards focus on what's important and not simply on what is urgent. Making it a priority and a habit to spend that unstructured time will pay dividends far beyond what you might imagine initially.