My 65 Fender Twin Reverb had a nasty hum for quite some time. I tried troubleshooting it many times with minimal success. Today, I watched a video that solved my problem in minutes without using any new parts.

The bad shield connection on the spring reverb tank was acting like an antenna and picking up the 60Hz signal from the power supply. A normal signal coming out of a reverb tank is only 1.9mV which means that the signal gets heavily amplified prior to reaching the final power output stage. Once the shield was properly cleaned and connected, the hum was gone and the amp sounds fantastic again.