Succesfully implementing Scrum

At my company they're now introducing Scrum. Traditionally most of our projects were done using a sort-of waterfall approach. But in recent years it has become harder and harder to get product releases onto the market in a reasonable amount of time using this approach, so management has been looking for a solution.

I have actually lead some projects in the past where we already used an iterative development process. Some of these projects have been immensely successful, while others have failed to deliver the intended result in a reasonable amount of time. I am curious to see whether following the more standard -and better defined- Scrum framework will result in more reliable success.

When I recently watched a Google Tech Talk where Ken Schwaber explains some of Scrum, he mentioned that only about 35% of the companies that try to implement Scrum actually succeed on doing so. And while everyone -including Schwaber of course- is very positive about Scrum's advantages, I haven't seen many details about what can make it fail. And more importantly: how to avoid the dangers that might make it fail.

In other words: how do we avoid becoming part of the 65% that doesn't succeed in implementing Scrum? Does anyone know?