The handle broke on the shut-off valve that services my dishwasher. The valve is soldered in-line, and in good condition - the pot metal handle cracked so that only the center cog remains. It is an odd configuration because the shaft has approx. 16-18 points on it. No replacement handle in the hardware store has this many. Most are 8-12 ppoint.
Is this a common problem, or is it because the valve is 30+ yrs old and they don't make then any more? Anyone with experience with these - ane where can I get a replacement?

I am having the same problem. My handles are oval-shaped chrome with 18 teeth splines. If yours have 16 teeth most stores carry them in a round format. I found a local Ace hardware that carried chrome oval handles but they had 16 teeth. You might just have to have the valves replaced to get working handles

Normally I would not recommend retro fit or generic faucet handles. They always seem to come loose.
However I recently was forced to use a couple. At Home Depot I found a set that seems to work. It was a set of chrome faucet handles that looked much like Price Pfister lavatory faucet handles I believe they are made by Danco.
The handle or knobs came in two parts. Part one was the chrome cover part, part two was a small clamp the is held in place around the stem with two small screws. Inside of the chrome cover has groves to fit around the clamp. Chrome cover is held in place with a screw into the end of the stem.
These seem to work because you can really tighten the clamp tightly.
Cost about 12$ for the set. While these are faucet handles they should work for you on a stop valve.