On Monday, July 1, 2013 9:39:07 PM UTC-7, Jeff Liebermann wrote:
1. Dirty battery contacts. Clean the contacts and possibly replace
the battery.

A freshly charged AA rechargeable didn't help.

2. Dirty test probe contacts, broken test probe wires, corroded test
probe tip. Clean or replace.

Testing the probes and leads was easy. Remove the black lead.
While holding the red probe on the black socket move the lead
in various ways. No correlation between needle movement and
lead movement evident. Likewise for the black lead.

3. Dirty rotary switch. Spray with a small amount of contact
cleaner.

The wiper-leaf-spring is held on the back of the switch with
one nut. That was removed and all the contacts were cleaned
thoroughly with a cotton tipped applicator. The dirt was only
some blackness left on the applicator. With the switch
reassembled the ohmmeter was dead stable again. Appears the
problem was just the barely visible trace of dirt on the contacts.

4. Dirty fuse contacts or bad fuse. Clean and/or replace fuse.

There is a spare fuse in plastic clips beside the working fuse.
The two fuses have about the same resistance. Swapping fuses
made no improvement.

Thanks to everyone for the tips, ... Peter E.