I know you've been using pods that have worked in the past but I finding the detergent manufacturers are messing with formulas again.
I Recently switched to the Cascade complete pods with Dawn and saw a very noticeable improvement in wash quality over the Finish tabs I was using before.
Try runinging a citric acid dishwasher cleaner first to clean out old lime scale and detergent deposits and then switch detergents.

Yes, I switched to a liquid detergent, cleaned the arms, the trays, the wheels, the filter area and ran a vinegar wash. Problem continues.

Don't you think that first wash water is supposed to be hot? I really think that is the root of the problem. But why is it happening?

Assuming your dishwasher is connected to the household hot water supply, there's no way it can get anything other than hot water ... but how hot is it depends on residual standing water in the line between the water heater and dishwasher. You say that you run the kitchen faucet to a confirmed hot flow before starting the dishwasher, but perhaps the dishwasher is fed from a separate line that's not tapped off the faucet ... or the physical mass of the dishware and dishwasher interior is absorbing much of the heat from the first fill such that the resultant temp in the machine is cool.

You'll have to check your user manual for details (if such details are listed there) but a Normal or Heavy cycle usually has two wash periods ... wash, rinse, wash, rinse, rinse for example. A light cycle or sensor cycle that doesn't find much soiling may run only one wash period.

BTW - first rinse is not necessarily supposed to be hot. It's really just loosening up the easy to get junk on the dishes.

If your DW is hooked up to cold water supply , this is what you'll get until the main cycle when the DW will heat the water to the correct temp, dictated by the program selected.

That's just the kind of info I needed, thanks dadoes and xedos. I noticed yesterday the detergent door doesn't open during that very first rinse and I thought perhaps the water was supposed to be non-heated. But the fact that this water is actually COLD, even though I've run hot water to the faucet, suggests either the dishwasher is connected to the cold water line, or more likely I think, this dishwasher uses so little water that the residual water in the line is all that enters during that first rinse.

Unfortunately, neither of these reasons explains why my dishes are coming out dirty. So jakvis, my next round of experiments will be with different detergents. I lean toward environmentally-friendly detergents and maybe they can't handle the job :(

The liquid/gel detergents are the worst performers for getting dirty dishes clean.
The enzyme based detergents are safe to use even with homes that have septic tanks and fields.
Buy a smal pack of Quantum or Cascade pods and try them I think you will see a very noticable improvement.

In the meantime Check and clean your filters and run a citric acid dishwasher cleaner like Dishwasher Magic or similar through your d/w to remove any deposits that build up over time.

The basic cycle on a European dishwasher is prewash, wash, rinse, final rinse, dry.

Your initial fill was probably the prewash, which is often not heated and you end up with whatever heat is left in the water after the tub and dishes have absorbed most of it. Only the wash, when the dispenser pops open, and the final rinse are heated. For really dirty dishes, the prewash might be heated - but the manual doesn't say anything about that.

Alex