Any radmon experts here? My unit has failed after water ingress

The scope traces look somewhat like a boost circuit. It's not easy to read the waveforms as the inductor clamps it to VCC and the transistor is switching ground. The ringing effect seen is caused by the magnetic flux in the inductor collapsing when the transistor is switched off. It looks OK to me. Some info on boost circuits here:  https://en.wikipedia.org/wiki/Boost_converter

I doubt dry joints. They are pretty rare these days and were most common in old vacuum tube devices and CRT TVs. They were caused by the high voltage and frequency breaking down the solder. Solder and other materials for components have come on in leaps and bounds since then so they are pretty rare. Your counter wouldn't have the current to start affecting the solder joints. A bad solder joint on the other hand is a different animal. Assuming you bought the counter as a kit and built it and soldered it yourself, you tell us. 

Not sure about the voltage to the tube. I use a 1 gig ohm / 1 meg ohm voltage divider to read the voltage at the tube. It works well and gives a fairly accurate reading when used with a 20 meg ohm meter. I can check on my GK Radmon later today and see what I get at the tube with just a meter. Did you alter the voltage pot? If not, then I wouldn't worry about it. If you did, you should adjust to get the voltage as close to the desired as possible. Too little and you are going to miss out on counts, too much and it could avalanche.

I have just checked my GK Radmon basic with my meter and I'm getting exactly 400v at the tube connectors, which is interesting as my meter isn't pulling the voltage down. My meter must be better than I thought!   Or the HV PSU has enough current to overcome the meter burden.

I forgot the voltage display was calculated from the PWM (even though I said just that a few posts ago!) If you haven't swapped out any parts, then it should be just fine. Looking at your graph it looks good. I think just let it run for a while now and see what happens.  I suspect it will just keep going. The fault may have been a bit of crap on one of the pin header pins for the ESP, or could be something else. Seems to be working, so if it ain't broke, don't fix it!

Solder doesn't really corrode. It's an alloy of tin and lead, so will form an oxide layer, which is why they go dull after a short time, but it doesn't corrode. It is worth noting that I have seen components of late that have iron in the leads. I don't think they used to. I think it used to be copper, although I could be wrong. You can easily tell by using a magnet to see if there is iron in the leads. Iron will corrode but is easily seen as it forms rust. The pin headers are usually gold plated so are fairly robust to the elements. 

Plastic is fine for housing the tube/counter. ABS/PVC/polycarbonate, they are all very suitable for the tube/counter and when used for background counting they won't block much at all. They will block alpha, but you aren't detecting that anyway, so all good I think.