Ezy, If you use the hairdryer, just be careful not to direct it straight onto the surface ie; 90 degs. Never know what might get picked up in the H/D & blown onto the mirror. Better off with a 'puffer brush' from the camera shop.
How bad is it? If it looks really bad, it may need a wash! Seeing as you have just recently purchased it, I would suggest using it for a while & if poss, take it to an open night or local club night for others to inspect.... A mirror has to be 'really dirty/dusty' to have any great effect on the quality of image. The contrast may be down a little, but you will not notice it.
My mirror has been 'washed' 2 x in the 12 yrs I have owned it.
I hope this helps a bit.
L.