CJ...your comment with respect to RFI (RF interference). My primary work deals with RF interference, "hardening" of equipment to keep RF out, and on the other hand, make antennas radiate RF energy efficiently.
Bypassing inside a microphone has to be done carefully. Bypassing the grid of a tube or gate of a FET with the high impedance involved will affect the audio. If T = RC (time = resistance x capacitance), the RC constant of 250 meg ohms or more paralleled with 500 pf changes the response of the circuit; the paralleled capacitor will also attenuate the output since it is in parallel with the capsule.
TN, how far are you from the radio station transmitter? If the RFI is AM broadcast and you live near the transmitter (3 km or so), you may get RFI and you probably can hear the audio in your equipment. You may get RFI from a nearby TV or FM transmitter but the programming will not be heard.
My suggestions:
1. Clean all connections on cable connectors. Oxidized connections rectify RF.
2. Use AC line filters (Ebtech's Hum-X, Corcom, etc.) on sensitive equipment. The purpose of this is to keep RF conducted from the AC power line out of your equipment.
3. Try a AC isolation transformer to power your audio equipment. Doesn't hurt to use a AC line filter on the primary side.
4. Are any cables 1/4 wavelength (or a multiple) at the transmitter's frequency? 984/(F in Mhz) approximates the wavelength; divide this by 4 for 1/4 wavelength. Resonant cables act like a tuned frequency receiver. Modifying cables can get time consuming so try 1-3 first.
5. If none of these works, then deal with the mic itself. Some mics have an output transformer; others are unbalanced, and some of them are differential out. Study the schematic first.
5a: Output transformer (normally 200 ohms): Connect a 500 to 1000 pf capacitor across the output transformer at the output XLR connector. If this doesn't work, connect 500 to 1000 pF capacitors to ground from pins 2 and 3 of the output XLR connector. Alternatively, you can put ferrite beads on the leads to pins 2 & 3 of the output XLR connector; make sure the ferrite beads are suitable at the nearby transmitter's frequency.
5b: Unbalanced audio (like AKG C60, Altec M30, etc.) No output transformer in microphone; audio from cathode follower is sent unbalanced to the power supply where there may or may not be a transformer. The impedance at the cathode may be 2 k or less. You can try 500 pf of bypass (to ground) but note if doing this "colors" the audio. If there is a output transformer in the power supply, bypass the XLR connector as above first. Alternatively, you can add a good quality output transformer in the power supply if one is not there. Most good transformers stop RF.
5c: Differential mode: Solid state transformerless balanced output: Recommend ferrite beads first. All connections at the mic should have beads since the audio rectification is probably occurring in the mic. Study the schematic. Be careful with these circuits...at the high impedances involved, bypass capacitors in particular may set the whole works into oscillation. Most of these mics are phantom powered. This means that beads are required on each lead of the XLR connector.
5d. If you live very close to the radio station (within the 1V/meter contour), this is called the "blanket contour" for AM, and one or more of the suggestions listed above is needed to keep the RF out of your gear. Speaker wires and RF: Suggest bypassing speaker leads with 0.1 uF 400 v mylar capacitors at the amplifier output. The twin lead running from the speaker to the amplifier acts like a doublet antenna. The inductive reactance of the speaker coil is high at AM broadcast frequencies so this looks like a doublet antenna terminated at the amplifier. You want to "short out" the RF at the amplifier or bypass it to ground. You don't want high levels of RF getting into the amplifier...in worst cases the RF rectified in the output transistors is strong enough to upset the bias on the solid state devices and cause failure.
CONSULT THE MANUFACTURER for suggestions also, especially for equipment in warranty. Mods to equipment in warranty usually void the warranty. You may need to call or email "up the food chain" at some of these companies to locate someone who understands the problem. Fortunately, I have encountered only one company in almost 45 years that was uncooperative.