I have recently added an addition on to my small home. The kitchen outlets are on two separate lines that are of the proper heavy gauge wire. The kitchen lighting is on a separate line that is of standard romex. Now when I turn on a hotpot or other appliance in the kitchen the halogen lights get brighter and other lights dim. Also when the well pump comes on, everything dims dramatically. This did not happen before.

The system did pass the preliminary electrical inspection, all connections are tight at the box. The only thing I have to do to complete the inspection is to install 15 amp breakers where there is standard romex and leave the 20 amp romex where heavier wire is currently used.

This sounds like a loose shared neutral connection, but according to your description of the branch circuits, you don't have any 3 wire feeders with a shared neutral.

If a subpanel was added, then the feeder to the sub may have a loose neutral connection, as indicated by when I turn on a hotpot or other appliance in the kitchen the halogen lights get brighter and other lights dim.

But the water pump causes everything dims dramatically., this is a 240 volt circuit with no neutral, and can indicate a voltage drop issue, cause by a loose connection of a hot leg.

Without knowing more detail, and assuming all branch circuitry is done properly,all I can offer is to have the entire service checked for loose connections, this includes the utility lines at the transformer and the connections at the house, the meter, at the Main breaker and the Main breaker itself.

Is the well pump new?

What is standard Romex compared to heavier gauge wire?

Is there any 3 wire circuits, such as the new circuits to the kitchen?

Did all you do is add a few circuits to the panel?

Is it possible that you disturbed something in the panel to cause a loose connection?

Is the main breaker a plug in type, that may be loose, or is it a bolt in type?

Not sure if I hit that actual problem but perhaps got you thinking.