My observations comes from my work with over 500 teams and the work of Hackman, Salas, Katzenbach and Smith, Lencioni, and others:
L1. The Five Dysfunctions of a Team makes some very good points, but it is important to keep in mind the book's sub-title: A Leadership Fable. Lencioni deserves credit for recognizing the importance of teams and giving people a framework for improving team dynamics, but there are no data to back up anything in the book and much of the advice contained therein is off base.
The last thing I would do with a top team is start an off-site with some sort of kimono opening exercise, like sharing MBTI results. HR might like to do this, but most C-suiters find these activities to be a waste of time. Top teams tend to be too action/results oriented to go for touchy-feeling team building activities. You build teams by having teams do real work.
2. Top teams should not be fully transparent. Some of the issues discussed at the top (strategy, potential acquisitions, succession planning, compensation, and the like) should not be made public.
3. Two of the fastest ways to impact top team and organizational culture (for good or bad) is through team member selection and operating rhythm changes. Who is on the top team speaks volumes about the CEO, and some flit from company to company with their entourage of incompetent sycophants. What gets discussed at top team meetings and the rules of engagement during meetings also affects team culture.
4. Followership is a critical topic for any team, and even more so with top teams. All it takes is one or two Criticizers, Brown-Nosers, or Slackers at the top to create a disengaged workforce and mediocre business performance.
You can read more about this in A Guide to Building High Performing Teams, a white paper featured on my LinkedIn profile or in The Rocket Model: Practical Advice for Building High Performing Teams (Curphy & Hogan, 2012).