If you do it right, you don't really have problems with dependencies itself. Also look at other package managers like Portage (Gentoo).
The actual problem, from an app developer point of view is that you can't ensure that the lib behave exactly in the same way as on the developers system (and that may not just because of different versions but also because of different compiler settings etc). In many cases, the app developer also has some own patches inside some of the libraries to integrate them better into his application. It is often utopic to wait and hope to get those patches upstream.
The actual problem, from an app developer point of view is that you can't ensure that the lib behave exactly in the same way as on the developers system (and that may not just because of different versions but also because of different compiler settings etc). In many cases, the app developer also has some own patches inside some of the libraries to integrate them better into his application. It is often utopic to wait and hope to get those patches upstream.