Positioning 3D Objects in place

The layers are not staying in place because the coordinates don't line up properly in 3D space. Hole your finger out in front of your face, then move your head around and look at how the finger floats over the background. The same thing is happening here. It's called parallax. 

You have to make sure the pins are attached to the surface of the map, not floating above it. That will be easier to do if the Anchor Point for your pin graphic is right at the bottom point of the pin.  You can then attach the pin to the map's anchor Point easily by holding down the Shift key and parenting the pin to the map. Then you remove the parent, stand the pin-up and face the camera using the rotation controls, then with the selection tool options set to Local Axis view you can drag the pin around on the map until it lines up with the right location.

This is even easier if your map layer is at comp center and you rotate the map layer -90º in X, then set up a comp camera and move it into position so you get a good view of the map. You can then add your pins with the anchor point at the point and just move them around in X and Z space. They will always be stuck to the surface of the map.

Parent the pins to your map and the map to the null for easier handling.

Also pay attention to put the pins on the map-plane, don't let them float above it. Check the alignment in side view (left or right).

*Martin