I have read the agile manifesto and spend a nice day surfing the web in search for this elusive answer. But sadly I did not get an answer that would cover all the bases.
When watching all the blog posts and newscasts of Agile preachers, you just hear about open scope or open "time" projects. How do you apply this to a fix cost project?
From what I found out the biggest problem is scope management. How do you determine if something is not inside the projected scope and how do you formulate arguments for your decision? Because of the agile way you are implementing your software there is no detailed design to argue upon. In most cases you only have a vague wish-list that the customer hands to you. And is so general that you can interpret any feature into it.
And with the rising percentage of fixed-cost projects this seams to me to be a real issue.
So the questions would be:
Scrum does not replace having proper requirements, or even having occasional major releases or milestones. Rather, it gives you a means to keep your team productive and focused, and avoids the time-wasting side-effects of a waterfall process.
In fact, one of the biggest advantages of an agile process like Scrum is that it causes you to "fail quickly and loudly" on problematic areas of your project. If, after a couple of sprints, your team still can't effectively estimate the time and resources needed to implement a particular feature, it may be worth pushing back on the requirements in that area -- they may need to be clarified, simplified, or scrapped altogether. In a traditional waterfall process, however, those "problem features" can often be pushed back to the last possible minute, resulting in the usual deathmarch and under-delivery into which most projects devolve.
However, the role of the Product Owner is even more critical in teams using Scrum who have a large set of requirements. Left to their own devices, most development teams will focus on the most interesting/fun/geeky features (service APIs, caching, search) first, and leave the "messy" stuff like payment process, UX design, and i18n until the last minute. A strong user voice is essential to making sure those features critical to the end user receive their fair share of attention.