Power quality is something that utility companies are starting to take seriously as they know the grids are loaded with motors, computers, digital electronics, variable speed motors, etc. What these do is poison entire neighborhoods with noisy ac power making the possibility of electronic component failure higher. They already shell out enough in spoilt food payments during blackouts and foresee more liability with power quality problems as well. Chances are that your utility has a power quality figurehead in a cubicle somewhere and they may very well come out and test. You can do it yourself, but the testing equipment costs thousands of dollars. Or you can try the bigger electrical contractors to see if they offer power monitoring services. But there's really very little you can do on the cheap to correct any utility power issue. The only way is a UPS/Converter system or a shielded isolation transformer for the whole house. You talking Lexus sticker price here.
As far as the air conditioner dimming the lights, that is normal to a certain extent. It the lights really dim, what that could mean is the a/c unit could have a worn-out start capacitor. This capacitor gives the a/c unit the surge it needs on startup and if it's bad then all the startup power is sucked up through your panel. If it's an outdoor unit, that draws a lot of current on startup normally. Also, tungsten light bulbs are very sensitive to small voltage drops so the effect is worse than it seems. One of the solutions is to increase the capacity of the house panel to 200-amps if it's already not that. This will lessen the effects of motor start-ups but not eliminate it. The reason is that the utility transformer serving your house is very stingy with current delivery and there is an inherent large voltage drop at your service panel. It's done on purpose so your house won't see a tidal wave of short-circuit current should one of your household motors short out.
Most power quality problems you can check and correct yourself are: the ground connection from your panel to the water pipe or ground rod should be tight and corrosion free,
the feeders at the main panel should be tight at the breaker lugs, the neutral bus should be bonded to the ground bus, the ground bus jumper bond should be tight, all circuit breakers should sit tight, breakers more than 20 years old should be replaced, all circuits should have their own neutral, all circuits with GCFI receptacles should be on a dedicated circuit. Also, these should be on dedicated circuits: refrigerators, microwaves and window air conditioners. Place these circuits at the bottom of the panel to minimize voltage drop to other circuits, especially 2-pole breakers for well water or septic pumps.
As far as testing, a simple 3-light plug-in tester will tell if you're wired correctly. Here's a hint: wherever you see junction boxes, open them up and make sure the wire connector nuts are tight and the grounding is continuous. Also make sure there's no electrical tape UNDER the wire nuts. That's about all you can do yourself without spending serious money.
As far as the air conditioner dimming the lights, that is normal to a certain extent. It the lights really dim, what that could mean is the a/c unit could have a worn-out start capacitor. This capacitor gives the a/c unit the surge it needs on startup and if it's bad then all the startup power is sucked up through your panel. If it's an outdoor unit, that draws a lot of current on startup normally. Also, tungsten light bulbs are very sensitive to small voltage drops so the effect is worse than it seems. One of the solutions is to increase the capacity of the house panel to 200-amps if it's already not that. This will lessen the effects of motor start-ups but not eliminate it. The reason is that the utility transformer serving your house is very stingy with current delivery and there is an inherent large voltage drop at your service panel. It's done on purpose so your house won't see a tidal wave of short-circuit current should one of your household motors short out.
Most power quality problems you can check and correct yourself are: the ground connection from your panel to the water pipe or ground rod should be tight and corrosion free,
the feeders at the main panel should be tight at the breaker lugs, the neutral bus should be bonded to the ground bus, the ground bus jumper bond should be tight, all circuit breakers should sit tight, breakers more than 20 years old should be replaced, all circuits should have their own neutral, all circuits with GCFI receptacles should be on a dedicated circuit. Also, these should be on dedicated circuits: refrigerators, microwaves and window air conditioners. Place these circuits at the bottom of the panel to minimize voltage drop to other circuits, especially 2-pole breakers for well water or septic pumps.
As far as testing, a simple 3-light plug-in tester will tell if you're wired correctly. Here's a hint: wherever you see junction boxes, open them up and make sure the wire connector nuts are tight and the grounding is continuous. Also make sure there's no electrical tape UNDER the wire nuts. That's about all you can do yourself without spending serious money.