The Breaker container has no mention of any panel. I can't see where the panel mentions any breaker type either. They are both QO (SquareD), and the type of clips that holds it in and makes electrical contact are the same. I'm just wondering why there is a problem. It's hard to find breakers for my panel, most I've seen have this hook looking type of clip

The only thing I can think of, is that 40 versus 20 amps could effectively be pulled though the breakers incoming hot rail connection point, that's it. And since the rail clips for both single and tandem breakers are exactly the same width, one can only conclude that a panel made for tandem breakers must have a rail that's more conductive. That's the only reasoning I can see. Is it supposed to start a fire as it sparks from 40 amps running across the connection? I just don't get it!

Is there an engineer handy?

Obviously I don't want to start a fire. The only other solution I have is to have a new service put in, which is beyond my abilities, not to mention the steep price tag.

Is it actually safer to have the single 20 amp breaker trip periodically? The wiring dates back to 1957 (not the Panel I believe, It would have fuses right) so the circuit covers several rooms, which draws more current than the 20 amp breakers limit? I figure it's better to add a 20 amp tandem and run wire for the second side, than to increase the breaker to 30 amps because the existing wire gage might not be able to handle 30 amps.

My plan is to increase the service rating (the MAIN breaker is 100 amps at this point) and rewire the entire house eventually.

So what's my course of action in the interim?