Think we can presume the company are already cheesed off with the cleaning and would think there are a few people there making noises over what has been written in the mirror, if it has been like that for a month, it must have been grotty in the first place. You are right that the owner takes the ultimate responsibility and it should have been checked by someone.
I have some sites that aren't up to my standard but the customer loves the cleaners so they get away with murder, other sites are pristine and the customer will pick up on the most tiny detail (had a big engineering company phone me once to say a mark had been left on the bottom of a washing up bowel).
Did she have permission to use the photocopier? Unlikely, even if she did, she was still using time you are paying her for to do her own work, at least she can't come up with the excuse that there isn't enough time to do the job, she has time to use the copier so she has time to clean the mirror.
Still say get rid, at the least it will show the customer you are doing something to put the situation right.
See Tim Downers back, where've you been?