The lights may start off dim or they may become dim then stay dim.

The dimming doesn't seem to occur when an appliance (i.e., air conditioner, washing machine, furnace, refrigerator, etc) comes on.

Some of the "dimming" lights are controlled by dimmer-switches and some aren't.

The lights that dim have the "old fashioned" incandescent bulbs; lights with CLF bulbs do not dim. (I do not have CFLs on dimmer-switches).