"I believe the guy put in 4/0 copper service conductors...." If you You mean PG&E then they usually install 4/0 Aluminum for underground service.
It could be a loose connection at the service point or in the service equipment.
is it one tenant that is having dimming lights or others are having the same problem?
It could also be that when a motor load turns on the lights dim, and probably it has been the case all along but she just started to notice it.
Does the apartment have elevators?
I would recommend you visually confirm the dimming and then install a recording meter and check for high and low voltage reading.
i am sure others will give you pointers as well.
