[UPDATE: I fixed the problem. See my reply, below, for details and suggestions.
NEWER UPDATE: Nope, not fixed. I've stronger spray, but I still have residual soap. See my latest post, please.

After years of reliable service, this 2012 dishwasher now USUALLY leaves some undissolved soap in the dispenser. (No change in the detergent used. No improvement when using brand-new detergent. Nothing blocking the lower rack. Water pressure is high. Dispenser does open.)
I have whipped open the door mid-cycle, and seen the lower spray arm rotate another few inches, but I cannot tell whether the upper spray arm is rotating at all. It seems to change position between peeks, but might be rotating slowly or intermittently. The arms are pristine inside. The sump area, including the impeller, is clear.
MY QUESTIONS:
(1) Might a stiffly-rotating upper arm be the problem? (It spins when poked, but not incredibly smoothly.) Shall I replace it, just to see? It's cheap enough.
(2) How can I tell whether the impeller is disengaged from its shaft, or if the pump is enfeebled? I can't find any service manuals for the "SHE" series.
(3) What other causes should I consider? Might there be a control-board problem? (I gather those happen, often from easily-fixed bad solder joints.)
NOTE: The hot water is, and was, via a tankless that hates low-flow appliances, shutting off below 0.5 gps, so the D/W has always needed to do its own heating. Using a clamp-on ammeter, I have confirmed that the DW's heater is functioning, at least when I'm looking.
THANKS MUCH for all the expertise this forum provides, and sorry for the long query.

Yes, for residual-soap problems, a clogged or blocked upper arm is the usual problem. But in my case, I got immediate relief when I replaced the circulation pump. That pump includes the heater, so it's often called the "heater pump". The part number was easily accessed via the parts diagrams at Bosch Home Appliances And you can find a Bosch 800 series dishwasher service manual online, which is very helpful.

NOTE TO ANYONE WHO DOES THIS WORK: Contrary to the service manual, you don't need to do a ton of disassembly, and fold down the tank, to get at this pump. I just put the unit up on bricks, to get a few extra inches, and could easily-enough remove/replace the pump from the back of the unit. But the service manual was otherwise helpful. It includes instructions to diagnose the pump (measuring the resistance), but be warned that my old pump wasn't doing the job, despite the fact that it metered out just fine. Perhaps the impeller, inside the pump, was damaged. But Bosch says that for these heater pumps you shouldn't disassemble the pump; you should only replace it. (The impeller inside the heat/circulation pump is different from the drain-pump impeller, which you can easily access from the sump, inside the dishwasher.)

Also, the instructions for running the test program, and for accessing the error codes, were impossible to find online, and AppliancePartsPros could not help. Turns out there was a single big sheet of paper under the dishwasher, with all that information, as well as wiring diagrams.

Now I know, and I hope somebody else finds this useful.

My dishwasher is working MUCH better. I did get some soap residue, but only once, and probably due to my blocking too much spray with unusual items. I'm going to replace my upper arm all the same, because mine rotates a little stiffly, and the new assembly is very reasonably priced.

Hi, as for the opening of the dispenser door, it always happens at the same time in the main programme, just after the water has attained working temperature. A relatively loud "pop" can be heard from the front of the machine.