[Radioroslyn]

As David mentioned there is a recommended maximum value for the input capacitor which is usually about 40ufd. The reason for this is that when the set is first turned on that capacitor being devoid of any voltage looks like a dead short to the cathode of the rectifier tube. This can put a lot of stress on the cathode for the first few seconds of warm up time. The higher the capacitance the more stress. Once the cap starts charging then that dead short starts to look like a resistor going higher and higher in resistance till the only thing that is drawing current are the circuits in the radio and not just the cap in that's p/s.

Hum can also be from leakage between the filament/cathode or cathode/control grid. Any AC voltage getting where it shouldn't be will cause hum. 

You could have the set near a strong magnetic field. Move it to different rooms in the house and see if that helps.

This modern age that we live in has so many devises that can wreak havoc on these old sets it's like a cancer. Take the signals produce by the average switching p/s used in a battery charger. They have a lot of amplitude and harmonics that can creep into the rf and IF stages. To the receiver it looks like just another AM signal. If we try to filter it out, then we filter out what we want to listen to also.

It's not unusually to have a little bit of hum. The older sets w/field coil spkrs were always more hum free than the resistance coupled filters that were used in the post war sets.  Back in the tube days you have ac (filament voltage) running around near high impedance grid circuits that can be influenced by this ac and cause hum. Now days in semiconductor audio and rf circuits there is no ac running around near the high impedance dc circuits. Thousands of microfarads of filtering and the dc coming out is clean as a whistle.

Another common occurrence with ac/dc sets is that with the set turned all the way down you can still hear stations coming thru. I've been told that it's from leakage in the diode to triode sections the det/1st audio tube.     

Enough of this boring stuff...