Typically,a radar gun is either stationary or moving in the same direction as the object to which it is pointed. However, when the radar gun is moving in the opposite direction and targeted at a vehicle moving towards it, does it really calculate the correct speed of the targeted vehicle? I ask this because the observed shift detected in the signal IS affected by the relative motion…thereby affecting the recorded speed. - Jinx
By the way, when asked in the past, the cops have stated that they do not issue tickets when they are moving in opposing traffic. But, as you probably already know by now…never trust the cops to tell the whole story. (Just like they claim they don’t have quotas to meet.) 
- Jinx
Yes, it will work correctly. The radar receiver looks at the direction of the frequency shift as well as the frequency differential. The unit takes into account the speed of the police vehicle. If the target vehicle is moving towards the police car (or if the police car is overtaking the target), the return signal will be doppler shifter to a higher frequency, and the unit makes the appropriate corrections. The same is true for the opposite case, when the return signal is shifted to a lower frequency.
Oh, and here is a nifty page explaining the exact calculations the radar unit performs in different cases.