Hi Gang,
Thanks for all of the suggestions.

Took a look at the schematic (damn, these are hard to read!), and
discovered that the screen bias on the finals is changed when in TUNE
and CW mode. Somewhere on the 'net, someone mentioned this as
causing a similar problem. Either the screen bias resistors are bad, switch
is dirty, or a connector is flakey somewhere in the circuit. I'll dig into
it and post the results.

For those that mentioned using an external key for tuning, on many rigs
that is how they are tuned, but according to the manual, the TS-820 can
be tuned using the SEND/REC switch in the TUNE and CW modes.
I'm not saying that the book can't be wrong, but I remember this is
how I tuned it many moons ago.

Steve W6SSP