Question for ya...if you turn the volume on the guitar to roughly half volume, does the "additional note" go down about the same? Second test,...turn the master volume down about halfway, does the "additional tone" do down about half". Then finally, try the same test by turning down your gain control. Don't do them all at once and don't pile them up...just one at a time. This can help to isolate where the harmonic or additional "ghost" tone is being amplified. We're looking for a response which is "non-linear". If it goes down about half volume when you turn the control down about half, you're not there yet. If it goes down a lot more in volume when you turn it down, you're on top of the amplifying stage that's responsible for bringing out the offender.
If the answer is no to all the above, you're introducing the tone to the input of the amp and it's doing what it's made to do...make it louder. On that note, if it's being introduced by pedals or external effects, simply take them out of the picture to be sure.
Anfotan is right, dried up caps can make a power supply sag. This can be a good thing as we all love our tube rectifier amps but that's done a little differently. Too much unregulated supply voltages and the amp becomes unstable and who knows what will happen. You'll probably eat up tubes and won't be able to bias them properly but it's been my experience that when this happens, they distort horribly and get real mushy sounding. They won't just act up during a solo.
Tubes...could be. Microphonic possibly but without hearing your problem it's hard to say. An old school check would be to get out a pencil, strike a chord then give each of the tubes a light tap. The thing will go nuts and ring out if you've got a microphonic tube.
Good luck...