[Tubesforme]

original coil was open and was replaced

Did the replacement have a rewound primary? If not could be it's starting to give up the ghost too.
A crummy ground is better than none. As it stands with out a ground it's getting it ground though the neutral side of the ac line via the line bypass caps. Try grounding it to the outlet and see if that helps. It's should make the vc work better (more control). It may not do anything about the signal level going up and down while the vc is stationary.

The replacement transformer was an original and not rewound. By the way I tried using my signal tracer to see where the problem might be. the problem is I live in Los Angeles and using the diode RF probe, on the tracer brings several strong stations, mixed, in together. When I disconnected the detector cap and connected it to the tracer, I had a good signal, however I didn't dare use much volume or it would distort. That is when I discovered that with just the signal generator ground connected to the chassis, the radio volume was better. The model 20 does not use AC line bypass capacitors. I also noted that the dial alignment is way off. I just ordered an alignment tool and will try grounding the chassis as well as aligning the chassis per the instructions that Ron Ramirez posted.

Just wanted to thank everyone for your suggestions. The problem was proper alignment and a ground as well as a longer aerial. I hope this also fixes the problem of the volume control acting like a noisy control after the cleaner has completely dried out. It just might be the ground that corrects that problem because the control is WW and one side goes to the chassis ground.