Lights dimming/flickering with any electrical activity

I live in an old house, have lived here for 20 years, and recently (within the past couple years), I've been noticing a lot of flickering in the lights when electrical activity occurs throughout the house. Originally, I thought it was a circuit problem, as the house was built in 1946 and had an inadequate amount of circuits: one circuit for three appliances (toaster oven and dishwasher on at the same time for example, would trip the breaker). This was recently remedied, with the washer/dryer put on one circuit, dishwasher on another, microwave on another, etc. But the flickering problem still occurs with all the lights in the house and now, it seems to be worse than ever. I used to only notice it when the washer was running: incandescent lights especially would react to it, pulsing and flickering with the action of the washer's agitator. But now, for example, if I have my desk light on and someone else turns the light on in the bathroom, my desk lamp will noticeably dim. It gets to the point where the flickering and dimming of my desk lamps alerts me to what other people are doing in the house. I can tell when the toaster's done for example, because my light will brighten right up! Surely this can't be normal. The wiring has passed inspections in the past, but the last one was probably over a decade ago. What could be the problem?