Anyone or any organisation that flies the flag of change management and improvement always has the difficult task of acting what they say, namely being a role model for what they espouse. It is difficult to get right all the time and I certainly don't.
One positive example I have experienced is the Institute for Healthcare Improvement who, a while back, took on the challenge of improving their invoicing and payment system on the basis they couldn't teach others to do it unless they (a) were a good role model and (b) learnt from their own experience.
The worst of management consultancy is when concepts and theories from books are copied onto PowerPoint slides and then used to train others. Where the trainers have no experience of the content their audience will soon figure out the dissonance and leave the session - either physically or mentally.
In England we have a rash of NHS Improvement related organisations trying to get onto the social media bandwagon. I am all for it as I believe it is an essential tool for communicating and engaging with others. However, when the organisations involved have no official and monitored Facebook page, do not use blogs (as in few is any of their Executive Teams or Senior Staff use them), have never used a wiki, do not use RSS feeds themselves as part of their own learning, or never used a discussion forum in-house etc - then the exhortations and training comes across as inauthentic.
There are one or two NHS Improvement groups, like NHS Improvement, who are using Web 2.0 techniques to their advantage and I like the way they are starting with themselves and learning how to use them in-house, before going outside. I am sure they will be excellent role models for the future.