What kind of problems would occur if polarity changes? We have had two rooms go out (that are in orig section of house ) and part of another room (in newer addition). Happened before. An electrician came out, wasn't having any luck and he heard a small "pop" and it starting working again. Now, 4 months later, it is off, again. Any suggestions? Thank you, Nina

If its now OFF and polarity changed, sounds like a loose neutral on that circuit.
Use an extension cord plugged into a good circuit and use for reference.

AC doesn't have polarity, it alternates between positive and negative. That is why it is called AC. There is a hot (ungrounded) conductor and a neutral (grounded) conductor. The hot conductor is non-white and the neutral is white. That's a physical thing and cannot get reversed unless some one reverses them. Most appliances don't care which is hot and which is neutral. The wiring is done a certain way for personal safety. If wired in reverse the appliance still works.

Indications are that you have a poor connection somewhere.

Go around and take note of all the outlets and lights that don't work. Turn off the breaker. Then again take note of all the things that don't work. You will then know what outlets/lights are on that circuit and which ones work and which ones don't. The poor connection or break is probably at the last working outlet/light or the first non-working outlet/light.

Remove a non working outlet. It is quite likely that you will find that it is wired using the "quick connect" holes in the rear of the outlet. If so, remove and rewire using the screw terminals on the sides. The 'quick connect" are known to develop bad connections over a period of time and can be intermittent.

If you do find the "quick connects" were used I recommend that you change all outlet and switches to the screw terminals. It will only be a matter of time before another short will develop somewhere else.
When trouble shooting be sure to check switches also. A poor connection at a switch can cause a outlet not to function simply because a wiring connection was made there.

The poor connection can be in the hot or the neutral. To determine which, do a voltage check between the hot and ground. If you have voltage, the poor connection is in the neutral. No voltage between hot and ground, short is in hot.

Be careful around light bulb sockets. If you misconnect the Black and White conductors, you will have the socket shell hot.

That means if you go to change the light bulb and touch the socket shell you will get bitten (shocked) the hot shell.

Just a Note, Polarity is a DC thing, AC testers will Indicating Reverse Polarity is usually when the Neutral is Hotter? Then the Neutral due to bad connections, and backfeeding through a load?
My Observation, Opinion.
HK is correct in the sense that AC has no Polarity. You can reverse the hot and neutral, it would still work, but in some instances it is not safe as Donf mentions about the Live Shell.

I have a real problem with an electrician coming in, hearing a pop then not investigating the sound source. Just not good practice. If there is a pop of any kind, there IS something wrong.

If everything is working, may not have been electrical related. It is hard to fix something that is now working, have you located the source or smell anything?