The main disadvantages to using a garbage collector, in my opinion, are:
Non-deterministic cleanup of resources. Sometimes, it is handy to say "I'm done with this, and I want it cleaned NOW". With a GC, this typically means forcing the GC to cleanup everything, or just wait until it's ready - both of which take away some control from you as a developer.
Potential performance issues which arise from non-deterministic operation of the GC. When the GC collects, it's common to see (small) hangs, etc. This can be particularly problematic for things such as real-time simulations or games.
