Since the problem is intermittent all you can do is replace the pressure switch and cross your fingers.

I would blow into the tube but in the tub direction.
Could be that there is a ball/mass of crud down there that partially plugs the tube once is a while. This would be a long shot.

[COLOR="Blue"] Perhaps it's full of crud. How do I check on that?[/COLOR]
You have to pull the inner tub out which is a real pain. I would replace the pressure switch first.

[COLOR="Blue"]Is that what I have to adjust to get the "full" level set on the new one? Can I assume that the switch, as bought, will already be set pretty close to how I need it to be set?[/COLOR]
It will be preset.

The tubing length is important as that effects the pressures but if the tubing is brittle etc. I would replace it. If the end that attaches to the pressure switch is stretched so it will not fit tightly on the new switch cut off about half an inch of it so it seats tightly.

OK, I figured it out. It was a bit trickier. Just a bit.

When you get an overflow, the first thing you think of is the pressure sensor. BUT, the thing to check first is the valves. That's what I should have done. Really trivial (which is why you should do that check first).

Start the fill cycle on WARM, so it's pulling both hot and cold water into the tank, and pull the plug. Pull the plug repeatedly. I just ran the line through an extension plug strip with switch. That made it easy to kill the power. If the fill stops every time you kill the power, your valves are OK. If the fill rate slows down suddenly, but doesn't stop when you pull the plug, you have a valve problem in one valve, and that's most likely what's making the overfill. In fact, that's what's most likely to happen if you have a valve problem, because it's very unlikely that both valves will fail together.

The valves should snap shut when power is killed.

That's what I did and, it appears my cold water valve is shot. What was confusing was that the fill stopped most of the time when I pulled the plug. But not all the time. That's not good enough! The fill has to stop EVERY SINGLE TIME you kill the power.

Now, having done this, you can check the pressure sensor as well by just blowing into it while it's filling. If that makes the flow rate decrease or stop, it's working. If the flow rate just decreases but doesn't stop, it's because one valve was bad. The pressure sensor feeds BOTH valves, so it it's working with one, it's OK. If blowing into the pressure sensor has NO EFFECT on the fill rate, and especially if you don't hear the clicks from the pressure sensor switch when you do, then the pressure sensor is bad.

Oh, by the way, after doing this check of the pressure valve, empty the tank completely before you reconnect the pressure valve hose. If you reconnect it when the tank is full, your next load is guaranteed to overflow, because there is no pressure in it.

All this being said, I went to the web and found my valve. I am stunned at the range of prices. I can get one for $16 (including shipping) from one source, and I see prices of $40-50 at other sources. These are all alleged to be factory replacements. What's the catch?

Actually, it wasn't that easy. The valve was flaky. Either after power cycling, or by itself after a few seconds, it would turn off. Once it went off, my agitation went fine, and the tub didn't flood. I never really had to close the knob on the house plumbing. If it was a situation where the valve always stayed open after the power went off, it would have been simple. It actually wasn't completely clear how long it should take for the valve to shut off. So when the valve shut off after a few seconds, I found myself saying "Well, OK." Of course, in retrospect, it should be immediate.

This is probably the most important lesson here. A valve may be flaky, and not behave reliably. Of course, it HAS to behave reliably. So all it takes is to see a valve failure once. That's a pointer that the valve needs to be replaced. If it "sorta" works, that won't cut it.

I never said it was only overfilling after agitation started. In fact, I kept the top open until the flow ceased, specifically to avoid an overfill. If the top is open, it isn't going to agitate. As a result, I had no idea if the timer had reached the point that it was commanding agitation. I didn't close the top until the valve managed to close itself, whether my waiting an extra few seconds, or by power cycling.

"If it did overflow at any time before agitation started, then there is something wrong with the water level system."

I don't get that. If the valve is stuck open during the fill cycle, it can easily overflow before agitation is commanded to start. If the timer tells the agitation to start, and kills the power on the valves, a stuck-open valve is going to stay open.