Here's what I would do:

Replace the switches. The outlets may be wired via the switch -- even if the outlets are not controlled by the switch -- so if the switch is failing or connection(s) through the switch are not solid, the outlets can fail too.

After shutting off the power, taking off the switch's cover, and pulling the switch the switch out of the electrical box without disconnecting it, take photos of all the wires and connections in the box. Buy a comparable, replacement switch and then wire it back up the same way the old switch was.

The circuit breaker isn't tripping because the switch's or connection's failure isn't causing a short. Rather it's causing an open circuit -- loss of power to the lights and outlets.

-- amateur

"I've contacted a number of electricians but I'd like to have guidance before they come"

Guidance? Yes. Let them do their job and if a number of electricians (however many that is) can't repair it,don't pay any of them and next time call only one because it only require's one for a job such as that.

I've contacted a number because I got an appointment with one, but I've contacted others hoping to find one who will be able to get here sooner. The problem seems to be getting worse.

If it's really a simple problem (like replacing the switches), that's great—but I haven't seen this problem described anywhere, and I've looked. So I asked for guidance hoping that either (a) someone here would know what is likely going on, or (b) I could get some guidance to figure out whether an electrician who shows up here actually knows what he's talking about, because I have a lot of experience with people who don't know as much as they claim to know, and I don't have an "in" with a good electrician.

Snark isn't really helpful.

Actually my intent was having you realize what you want isn't possible. To appraise another's techniques and technical knowledge require's the appraiser to have at minimum equal or more experience than their subject. It's the equivalent of hypocrisy in daily life. To cover all your bases the best you can do is ask for proof of licensing. If you simply want to elevate yourself in the the electrician eyes,tell him you suspect the house was wired with aluminum and wire nuts are beginning to loosen after all these years. Even if it turn's out wire is copper,he will find loose wire nuts and/or bad connections behind those switches you've been wiggling and consider you to be far above average homeowner when it come's to electrical troubleshooting. Do not tell him a guy on the internet told you this or he will think you are just another ,,,,,,well he woun't think you are all that smart after all.

That is a much nicer answer, thank you. And no, I wouldn't say that to anyone!

I'm sorry to say that my experience is that sometimes you absolutely can tell when a pro doesn't know what they are talking about. I might not know the correct answer, but sometimes I can identify an incorrect one, or at least identify someone who doesn't understand the principles behind what they're talking about.

The main thing I don't understand is how a problem switch could cause trouble on multiple circuits, and why it is getting worse. Yesterday the air conditioner started going out during these moments as well, and we didn't even think the a/c shared same circuit box.

Which brings me to the other reason I posted: to give someone a chance to say, this is an emergency, don't wait for calls but call an emergency electrician. And that's another reason I had tried to make contact with several electricians, hoping to be able to speak to a human who understands these things enough to know how urgent this is or is not.

There should be no jiggle in any switch. If it's the toggle and internal connection of the switch, it's an easy fix of a new switch. If it's the whole switch jiggling the wiring behind it being backstabbed or capped in the box, that's worse as there are loose connections. The pig ears of the switch should brace against the wall finish, and the coverplate can help hold the switch from sliding back n forth.

Not to scare you, but weird things happen. Last August, my friend started having problems with lights flickering in different areas of his house. It didn't make sense to him, and was getting worse, so he called the power company to see if there was a problem with the lines. A guy from the power company came out and said there was a problem at his circuit box and that my friend should call an electrician. He didn't act like it was urgent, but suggested not waiting too long. Luckily, I had another friend who was able to recommend an electrician -- called him and he said he'd come out and check it the next day. The electrician showed up and apparently told my friend he couldn't believe that the power company didn't cut the power IMMEDIATELY! He said it was terribly dangerous... there was a water leak to the fuse box and a voltage imbalance on sides of the house and at least one of the breakers had fused, so no matter what happened, the breaker(s) couldn't trigger. The electrician called to have the power cut immediately (what an operation that is!) and then proceeded to replace the entire circuit box.

Of course it's an emergency. At this rate of things failing you will soon be in the dark and have food spoil and worse case there might be a fire or someone electrocuted. After hearing about hvac,I'm thinking the neutral might have failed and current is now flowing on ground wires.

I can't overemphasize the urgency of having it checked out.

ah, yes, the ground wires. The electrician told my friend that the local cable company is somehow the one who installs the ground wires around here, and he said they always install them incorrectly. He replaced all of that too.

Over the past 18 months mining and production of copper slowed and demand drove retail and scrap prices to all time highs. Copper thieves removed wires connecting transformer to plate on bottom of pole on several poles in an area resulting in hundreds of homes losing earth ground. An unattentive lawn tractor or z-turn operator can easily damage ground rod wire at meter.

Thank you to everyone. I tend to under-react rather than over-react, which can be a problem.

Now the problem is to get someone's attention so they will come! I have spoken to an answering service but still haven't heard from any actual electricians, or gotten an appointment before tomorrow.

It's very easy to replace the switches so you should do that ASAP (unless the electrician is coming today or tomorrow). Follow wdcruise's procedure (the first comment).