In essence, a radio receiver is a filter and a rectifier. Any trace or wire can act as an antenna. A good ground will help you recieve a stonger signal. So you have to track down where the RF gets in.
Long lines on the control pots?
You need a number of strategies to deal with unwanted signals. You need to understand the source of the problem and its remedy.
How does the interference get into your system. Electromagnetic, Electrostatic, Grounding errors, poor insulation, optical, vibration, proximity?
It’s hard to say if particular elements are more sensitive because it depends on the topology of the circuit. In general you need to keep the big signal stuff away from the small signal stuff. This is requires a combination of physical and electrical isolation.
Avoid long loops for both signals and grounds. Use local decoupling. Don't connect opamp summing nodes to long lines. Current doesn't take the shortest path to ground, it takes all paths.
The lower the impedance the more preferential the path.
How to fix it. Shielding, Filtering, correct grounding, layout ,mounting.