This has happened before, and I'm in mirror mode just using a reference picture, and I now I notice that the other side is in a faded color. And I cannot click it or interact with it.
It is by design. The other side will only be available for direct manipulation after you have applied the modifier. Mostly, when a user attach a mirror modifier, it's purpose is so that the user could just focus on working on one side of the model until we need to break the model's symmetry.
The greying out give you a visual as to which side of the model you are currently suppose to work on as you rotate around the model. You can imagine it would be frustrating to be clicking on something that is inactive by design.
As hawkenfox said, it is by design. However, there is a way to allow the other side of the mesh to be interacted with (warning, it behaves a little strangely). It is toggled using the mesh-triangle icon in the top bar of a modifier.
This mode won't quite let you interact with the other side of your mesh normally. All that it does really, is select the corresponding vertex on the non mirrored side and let you move that. As a result, the control widget will be over the original side of you mesh always, and you cannot perform transforms between the sides of the mesh. (You couldn't scale to verts on opposite sides together for example)