Spencer, low level hum is a common problem if you are putting your ear to the speaker. SETs usually use a directly-heated cathode, which is to say that the filament of the tube and the cathode are the same thing. This means that you have to have a DC supply if the power tube is not going to hum; getting the DC supply to be quiet suddenly becomes an issue!
RF issues are often caused by lack of what is known as 'grid stop' resistors in the circuit or issues in the grounding scheme of the amplifier (I'm talking about how the grounds are laid out inside the amp, not outside). If the RF is rectified, you will hear the station, and it is well-known for also causing hum.
Have you noticed the RF with any other amplifiers?
RF issues are often caused by lack of what is known as 'grid stop' resistors in the circuit or issues in the grounding scheme of the amplifier (I'm talking about how the grounds are laid out inside the amp, not outside). If the RF is rectified, you will hear the station, and it is well-known for also causing hum.
Have you noticed the RF with any other amplifiers?