Couple of things I have found with similar circuits and problems.
If you doubt your power source, try in on battery.
Sometimes it is worth putting a low value resistor in series with the supply at the device, and a large electrolytic behind it. Doesn't apply to high current circuits.
Also any wires to the pots that set the frequency can pick up hum, so they should be short and maybe screened. I found on one circuit I was using a varicap for tuning, putting my hand near the circuit and another hand near a desk light made speech on the receiver unintelligible.