I managed to remove most of the noise from the mirror but I'm not quite sure what caused it because I have done lots of things:
-changed all materials with non-physical properties like reflection level or glossiness 1,0 to about 0,8
-lowered a bit intensity of sun and sky
-changed sampler from 5D deterministic to 5D High-D
-changed shower glass material from one-sided to solid as it is a two-sided mesh (with thickness)
-changed mirror's diffuse level to 0,0
Now in my scene there is only one thing that adds this ugly noise to the mirror:
-changing mirror's material's diffuse level to more than 0. If you change it even to 0,1 then the noise appears
So it looks like adding diffuse to mirror-like materials creates these fireflies when there is lots of contrast in the scene. I think it needs fixing if it's possible.