Dangerous vintage radios
Pat--I was talking about AC/DC radios above. Many of these had a huge safety problem. Thankfully, it's easily dealt with.
AC/DC radios were designed to have no AC transformer. This was a cost cutting move. AC/DC radios were usually the cheaper radios on the market. They were very common--almost every radio I've seen from the 40s or 50s (except console) is AC/DC.
Due to the overall AC/DC radio design, the metal chassis (holding the electronics) is never very well isolated from the power cord. In some cases, one side of the power cord is even directly attached to the chassis. Thus, the chassis on one of these radios CAN be live. Someone touching the chassis could get a nasty shock. Or even be electrocuted. This applies ANY time the radio is plugged in, whether or not it's on.
Touching the chassis accidentally was too easy in the early days of AC/DC radios. Back covers had huge openings through which even an adult hand could slip in. The chassis was held in place by screws underneath the radio. These radios are the ones I'd consider potentially dangerous.
Later on, safety standards apparently improved. These improved radios had a chassis fully enclosed by the cabinet, with no exposed chassis screws, and vent holes that were too small for even the smallest finger to slip in.
In order to fix the live chassis problem, particularly on the older AC/DC radios, some experts suggest a couple of changes:
-Installing a polarized plug, which, when plugged into a properly polarized outlet, will ensure that chassis side is connected to the neutral side of the power grid. (Although, one needs to be sure the wall outlet is properly wired!)
-If necessary, rewiring the power switch so it's on the live side of the power cord
Radios using an AC transformer should not have any live chassis issue, since the transformer should fully isolate the radio from line voltage.
The worst AC/DC radios were probably some of the earliest. I've never seen one, but I've heard in the early days some used a special power cord that included a resistive wire to help with the voltage drop. These cords ran hot, and could even start fires. I heard they were called by some "curtain burners."
Link to article about AC/DC radios, which more fully describes the issue. Plus instructions on how to rewire an AC/DC radio (for those competent to take the task on):