There are two problems with milestones, that stand out for me:
1. The proud nail part is that they are not very adaptable as a mechanic. The concept is easy enough to adapt to various styles, but the mechanics don't give you much to work with. And that directly ties into the second part ...
2. Milestones represent a failure of nerve. They are too weak to do what they set out to do--which is to encourage continuous play, but too ticky-tacky in their implementation to blend in seamlessly with everything else.
A truly great mechanic is one that is subtle in appearance, but profound in its implications and effects. Most mechanics will fall short, but Milestones manage the amazing trick of precisely reversing that--an "in your face" mechanic that does very little. Contrast this, for example, with something like healing surges--in your face, but also very strong at doing exactly what it sets out to do. Or at the opposite extreme, combining various skills into Athletics--not terribly important, but nonetheless with real, subtle implications.