Vibrating Mirror

Many thanks to Ian Gray for this solution.

Remove the plastic cover which sits ,over the roof to mirror mounting screws , Small screw drive required for this to gently "flip" it off.
Remove all three of the mounting screws to release the mirror arm from the roof.
Remove the central screw holding the plastic spacer onto the mirror arm mount.
Super glue the spacer back onto the arm and quickly refit the central screw , nice and tight but not enough to crack it.
Refit the mirror back onto the roof mount with the three screws , again quite tight.
Leave this fully to dry , 24HRs is best.
Now fully test will a fast motorway drive and you will find the vibration has disappeared and all police cars now become clear.!!!

Not one but two solutions (we are spoilt ;-). Thanks to Roger Collier for this one...

As an experiment I took a small plastic rod, 3.5 cm long and wedged it between the glass and the hole in the top of the mirror support, with a lump of blu-tack at each end. Result - no more vibrations. An elegant and permanent solution would be a stick with a sucker, such as a child's toy dart or arrow cut to size. Roger the bodger.

(The ISDC cannot be held responsible for any modifications that adversely effect the warranty of your car.)