Yep, there is all sorts of whacky low frequency noise floating around. Power supplies, switching regulators, leakage out of spectrum analyzer, building AC ground floating above earth ground, stray industrial equipment noise (like induction heaters), ground loops, high impedance pickup on Vtune lines, wireless transmitters, etc etc.
A good tool to have is a battery box, where you have a big battery, and a 10 turn potentiometer with a 10 uf ceramic cap across the output, and use that to be your Vtune supply whenever you think you have a real spur and want to check it.
And don't throw away those old HP analog power supplies--you might need them someday to finish up a test (just check them before using to make sure their old capacitors did not fail and cause unstable output voltages!).
Rich