What are the most common mistakes in implementing lean?

To start with, lean must never be seen as a tool for headcount reduction or mindless cost-cutting. This fundamentally misses the purpose of lean, which is to create value through eliminating waste. As companies improve their processes they should be able to reallocate their productive resources to new value-creating work.
Another important attitude to avoid from the beginning is the impulse to implement individual lean tools without seeking to understand the system in which they fit. This is hard to avoid, since many tools, like 5S, deliver immediate payoffs. But ultimately all lean workers must understand the "why" behind the tools, or their value will be lost.
Lean beginners should also limit the scope of their initial project so as to better insure success, be sure that they have a leader with deep knowledge and a gemba attitude i.e. always base one's thinking on a close observation of the work itself, and never relax in their efforts. Indeed, one of the hardest challenges they will face is the degree to which individual lean successes will invariably uncover new problems and greater challenges. So in this regard, simply be aware of how difficult this work will be.
There are more detailed responses in the article Misunderstandings About Value-Stream Mapping, Flow Analysis and Takt Time about other common mistakes, by John Shook and Mike Rother.