If the metal frame isn't grounded, then you may well be getting a practical demonstration of capacitive coupling. (See? It's not just theory! [Linked Image])

Yes, a great many normal household appliances will work perfectly well with hot and neutral reversed. Over in Continental Europe many countries use a standard appliance plug which is reversible (even the grounding type).

Many old radios/TVs (both in the U.S. & U.K.) were "live chassis," meaning that one side of the cord went straight to the chassis. They were designed so that no part was exposed to touch, but it was still best to ensure that the chassis went to neutral. It's also why we use an isolating transformer when servcing this type of equipment. Although live chassis went out of favor, it has made a slight comeback in modern TV switch-mode power supplies.

With swapped connections, any single-pole switch will leave the bulb, element, motor or whatever hot when off. There's also the point that an in-line fuse (as used in mUch line-powered electronic equipment) will end up in the neutral, so the house breaker will be the only protection against ground faults.