While I don't disagree that it's a good idea to use distilled water for anything involving a solution (dev, stop, fix, etc.) - exactly what advantage would distilled water have for interim phases? For instance, stopping with a water bath or rinsing/washing? I'd figure that as long as the water is in transition it's not really going to affect the film. At the last stage, then one could use PF+DW on the final rinse.
You know, I'll probably never be able to answer that question with any real certainty. It would take a fully staffed and equipped research lab to get to the truth; who has the time or resources?
For the record, I thought that the interim steps didn't matter either. But I was being methodical (old engineers are like that) and testing
everything trying to get rid of the grunge. And this is
after I'd done all the "normal" things like washing down the ceiling and walls, cabinets, etc (you wouldn't believe how much dust you'll find on the underside of a shelf, or on the ceiling, until you clean them). I had everything spotless, the darkroom was completely sealed, an air cleaner running, etc. but I was still getting grunge on my film.
So I went to work on my process. First I started with mixing stock solutions with steam distilled water. More improvement. So I knew that there were process problems. I went to one-shot developer use. More improvement. One of the big improvements was to use my fixer as a one-stop. Turns out that tiny bits of silver can precipitate out of used fixer, and the next time you use that fixer they can stick to the film. This was news to me.
Eventually I ended up with tap water in just two places. Dilution of the developer, and washing. Ninety percent of my problem gone, but 10% still hanging in. So I replaced all the water with distilled. Now I've got about 98% gone.
What I
think was happening is that I have a fair amount of scale in the pipes just because they are old (this subdivision is 50 years old and the city is starting to tear up the streets replacing both water and sewer pipes). The scale is small, but solid. And it appears to stick to the wet glue that we call an emulsion. Once stuck, no amount of washing gets it off.
So... All I know for sure is that the less tap water I used, the cleaner my film became. What I don't know is why -- I can only speculate. But really, I don't care that much because of the results.
I thought about putting filters on the hot and cold lines, but I had trouble finding filters for small stuff, say down to 5 microns. Before you scoff, I like to enlarge, sometimes over 12x. So those tiny spots become visible - think tiny black dots randomly placed in a nice smooth sky. Painful to my eyes anyway.
What stopped me from going the filter route was a) distilled water is cheap, b) filter systems are expensive and require periodic maintenance and consumables, and c) they don't do anything about the scale in the lines *after* the filters and up to the tap. Any plumber will tell you that the inside of copper pipe, especially if it's got a bunch of solder joints, ain't pretty.
So... it might just be the placebo effect (I did run an extensive series of tests because I couldn't believe it myself, but still...). Yet it's costing me less than $0.10 USD per sheet of 5x4 film in distilled water charges (IOW, it's raised my film/processing costs just 7% while reducing my spotting time to almost nil and raising my photographic happiness immeasurably), which is considerably less than the cost of a filter system would be.
In all, it's a risk I'm willing to take. Especially since it seems to be working.
After being hammered to descale, flattening and folding, it also made a nice 12lb counterweight for the enlarger. 
