Mirror with sconce lighting cracked
How often do these types of mountings cause problems like this?

There is no way to answer that. In my opinion there is no way to prove that your employee caused the crack.
The genesis of the crack is the opening that was cut in the mirror for the light fixture.
It may be that the crack  just happened without any outside influence, perhaps it was not a perfect cut,  the cut caused a weak spot.  Or the light fixture was tightened down a little to much and over time the opening in the mirror just failed. Or, Or.
If cleaning the mirror caused the crack to start then it would be because there was no proper support behind the opening, resulting in the glass flexing during cleaning, as opposed to not flexing because there was proper support behind the opening.
There is not much we can tell you,
Try to explain to the owner about where the crack started and why a hole in a mirror needs proper support behind it or how it there are inherent risks in cutting glass .
If it were me and  they want take legal action then i would tell them that   i would take my chance at having a court listen to both sides.