Some radios and amplifiers didn't even have a power transformer- I can't imagine how many people were injured or killed by those.
Most electric devices made before the mid-'60s had an un-grounded power cord and one example of dangerous was guitar amps, which not only were un-grounded, they sometimes had a switch for reversing the polarity of the power connections. The switch had a capacitor on the polarity switch that's usually called the "death cap" because it could fail shorted and cause the chassis to be electrically 'hot'. When these amps are restored/serviced, a grounded cord is installed, the polarity switch is disconnected and the amp is usually safe but people have died or almost died because of this, including Keith Richards (Rolling Stones) and Keith Relf (The Yardbirds). I don't know what these switches have against people named 'Keith', but.....
A good indicator that something is wrong comes when touching the chassis of audio equipment and feeling a slight tingle or strange vibration when sliding a hand or finger along a metal piece, like the face plate of a receiver, pre/power or integrated amp when standing on concrete, especially without shoes. With a guitar amp, touching the strings, the cord or the amp can result in tingling when on concrete and it could be the amp or the electric wiring. I have experienced this in both cases and it's no picnic. If a guitar player has one hand or forearm across the strings and grabs a mic or touches it with their mouth when singing, arcing can be seen and grabbing it can cause the current to pass through the person's heart.