Had very similar issues, in one case I had a stray earth, had used shielded wire and one of the hots wires was intermittently earthing out, in the other the bridge earth had come lose. Wiggling the lead, if your touching the metal of the jack will reduce the noise as your effectively becoming a conduit to earth.

If you have a multi meter I'd start by checking everything you expect to be grounded is, and there is no stray wires, solder between pot connections.