Do any lights get brighter at the same time as other lights get dimmer? The neutral at the power company's transformer could be bad, and no amount of solid ground connections in the customer's house will help that. The power company would have to fix that.
Do the lights in neighbors' house (fed by the same transformer) also dim, and at the same time? In addition to the above possible bad neutral at the power company transformer, could be a bad connection on the primary side of the power company transformer, which obviously you don't want to touch!
