If the raw plugs are not holding the mirror, you could consider using a Polyester Resin to secure the fixings in place...one of our customers did this and sent us the photo - I have tried to attach it!
//www.diynot.com/network/skilledbuild/albums/
Customer used a Vinylester Resin to Fix fittings into wall for a heavy mirror.<br><br>http://skilledbuild.co.uk/resinfix/resins/ultra-rez-vinylester-resin.html
If the DPC needs looking at, you may want to consider a chemical damp proof product which you inject into the mortar joints or brickwork...
Agree with previous comments though looks like classic efflorescence!