hmmm.
Peaks and dips? Sounds like something in your circuit is acting like an antenna?
OR the source you are driving it with has harmonic RF output, so try a battery driven potentiometer...with heavy capacitive shunt filtering.
try floating the chassis ground on your spectrum analyzer where it plugs into the wall.
realize that the KTBF noise of a 500 ohm resistor will be VERY small....so it would be hard to actually see it on a spectrum analyzer with the thousand other noise sources in your lab.