[Jason63]

Indeed I meant to say "full wave rectifier" and not "full wave bridge rectifier" -- I corrected that. Either way the output has a 120 Hz frequency component which led me to suspect it. In fact I'm still convinced this is the source of the hum, though thanks to Morzh's suggestion, I believe I've found the source of the problem.

Moving the radio to a different position had no effect on the 120 Hz hum. However, rotating the frame antenna inside the chassis did have a significant effect on it. In particular, whenever the wires from the frame are near the speaker, the hum is significant. And when they are as far apart as possible it is essentially gone. Unfortunately, it wants to rest in a position with the wires near the speaker, but I think it will be easy to use a wire tie to hold it in the correct position to eliminate the hum.

I'm guessing that the 120 Hz ripple current going through the speaker's field coil is being radiated by the metal body of the speaker and this is finding its way into the front end when the metal frame antenna passes near the speaker. I can certainly try a few more things to confirm this, but it's nice to at least be getting closer to solving the problem.

I do notice a tremendous amount of noise on the lower end of the AM radio dial, but it is not a 120 Hz hum and is very different in character. I think this is the EMI from all of the wall-warts, CCFLs, and other devices that have been mentioned here and are common around the home these days.

Thank you everyone for your ideas and suggestions. If anyone has any other ideas for me to try, I'm happy to give it a try and report back here. Otherwise, I'm inclined to call this problem resolved.