I picked up a 1977 LabSeries Guitar amp and it picked up radio stations as if it were designed for it. This is how I fixed it.
Watch the video in this log entry :)
The tricky part about this is you have to find out what part of the amp is acting as an antenna. In the case of this amp, it was the wire that ran from the amp head down to the reverb tank. I found this first by using some cheap aluminum foil.
With the foil grounded via a wire to the amp chassis, simply move it around the amp to pinpoint the location that is picking up the signal.
After you find out the side that is causing the problem, wrap the offending wires with the foil. This creates a makeshift shield as long as the foil is grounded to the chassis
If you want to keep the amp original, and not replace wire, you can leave this foil in place. This is fine as long as the amp isn't really moved. However, if you move the amp around you will want to replace the foil with something a lot better. I chose "Slug and Snail" tape as it was a tenth of the price when compared to the copper tape that music stores sold.
If you don't mind replacing wire in the amp, you could pick up some shield wire and replace it, remembering to connect the shield to a ground.