I have always struggled to convince people who have been hard trained on Continuous improvement that Innovation is not about process improvement. It is about questioning the process itself or questioning the efficiency or relevance of the process. If you keep looking at only improving the existing processes, beyond a point it will not achieve anything.
I am happy Ron Ashkenas in his HBR blog writes about rethinking the continuous improvement. I agree with almost everything that he mentions in this post. Last point needs a special emphasis. In my experience people are so much blinded by tools like six sigma that they refuse to think beyond them, they fail to see that they are capable to designing the best processes for themselves. They fail to realize their own creative potential and get imprisoned in the success these are said to have created for their parent companies.
Customization of continuous improvement is also important. Every industry, every organization has its own way of doing things, its own environment and hence all such tools must be aligned with that for the optimized results. More often than not the tools are picked up as best practices and used blindly without evaluating their relevance for the organizational needs and characteristics.