@kellogs suggestion of MVC is valid, and used in a few games, though its much more common in web apps and frameworks. It might be overkill and too much for this.
I would rethink your design, why does the Player need to talk to Enemies? Couldn't they both inherit from an Actor class? Why do Actors need to talk to the Map?
As I read what I wrote it starts to fit into an MVC framework...I have obviously done too much rails work lately. However, I would be willing to bet, they only need to know things like, they are colliding with another Actor, and they have a position, which should be relative to the Map anyhow.
Here is an implementation of Asteroids that I worked on. You're game may be, and probably is, complex.
