Sorry, it was not meant to sound nitpicky. I was surprised that I actually had never stopped to think about Moon's rotation, and that maybe it did not spin to a stationary observer.

The more you know...

As long as you're onto spinning things, check out Mercury's rotation.

Moon rotating has nothing to do with from where the observer is observing it. An object is rotating if it produces centrifugal force.

Circular motion can be thought of as analogous in many ways to linear motion. Consider that you are on the surface of Earth, which is rotating. Therefore you are also rotating, however relative to Earth, it makes sense to say that you are not rotating. Similarly with the moon. If it were rotating relative to Earth, then we would expect to be able to see what is on its current dark side, as it would be the lit side after half a rotation.

Also, a rotating object does not need to produce or receive any force. The conservation of angular momentum says that unless a force acts on a system, it will continue to rotate at whatever angular velocity it is currently rotating at. This is because the system itself is not accelerating. If you look at a particlar subsection of the system (say at an end), then that subsection is accelerating due to a centrifugal force, but that force is contained within the system.

This isn't really accurate. Circular motion is absolute, but linear motion is relative.

Even on the surface of the earth you can tell you are rotating, even inside a completely closed room. For example with a http://en.wikipedia.org/wiki/Foucault_pendulum

Or rather, the other way round...