The extension cord trouble is not caused by a short, but a poor connection somewhere at that point: either the extension cord's connection to the socket where it's molded in, or the spotlight's plug connection to its cord, or the interface between the two (dirt, looseness in the socket so it doesn't grip the prongs of the plug well, etc.) The poor connection leads to higher resistance or arcing, both of which dissipate power and that creates heat that melts stuff.
A hot shorted to a neutral would cause the breaker to trip (very nearly) instantly. If it doesn't, the breaker is dangerously bad and needs to be replaced. Standard household circuit breakers are "thermal-magnetic" circuit breakers and have two mechanisms by which they trip when there's too much current: first, the thermal part, which responds relatively slowly to small overcurrent situations, and is basically a bimetallic strip similar to that in a thermostat or thermometer that the electric current passes through. More current passing through it means it heats up more and bends more, and eventually it bends enough to trip the breaker mechanism and shut off the power. This allows a modest overcurrent for a short period of time without a nuisance trip, such as might be expected from a motor starting up. The other trip mechanism is the magnetic trip, which responds instantly at a higher current and consists of a little electromagnet triggering the trip mechanism. More current through the electromagnet means a stronger magnetic field, and at some point it's enough and the current gets shut off.
Theatrical dimmers often have on their outputs just magnetic breakers, which don't suffer from different response characteristics as they get warm. The little breakers on power strips are often thermal only (and often are of slightly dubious reliability, though that's not as much of a worry since the circuit the power strip is plugged into is presumably protected properly by a proper breaker or fuse).
Please make sure the system does not get used at all until thoroughly inspected and repaired as needed by a qualified electrician. I hope it's not the case, but I would not be surprised if there are further issues that need to be addressed, hopefully just simple things like snugging up connections that have worked loose over the years. Your life, your cast and crew's lives, and possibly your audience's lives in case a fire should start are worth any inconvenience it might cause.
A hot shorted to a neutral would cause the breaker to trip (very nearly) instantly. If it doesn't, the breaker is dangerously bad and needs to be replaced. Standard household circuit breakers are "thermal-magnetic" circuit breakers and have two mechanisms by which they trip when there's too much current: first, the thermal part, which responds relatively slowly to small overcurrent situations, and is basically a bimetallic strip similar to that in a thermostat or thermometer that the electric current passes through. More current passing through it means it heats up more and bends more, and eventually it bends enough to trip the breaker mechanism and shut off the power. This allows a modest overcurrent for a short period of time without a nuisance trip, such as might be expected from a motor starting up. The other trip mechanism is the magnetic trip, which responds instantly at a higher current and consists of a little electromagnet triggering the trip mechanism. More current through the electromagnet means a stronger magnetic field, and at some point it's enough and the current gets shut off.
Theatrical dimmers often have on their outputs just magnetic breakers, which don't suffer from different response characteristics as they get warm. The little breakers on power strips are often thermal only (and often are of slightly dubious reliability, though that's not as much of a worry since the circuit the power strip is plugged into is presumably protected properly by a proper breaker or fuse).
Please make sure the system does not get used at all until thoroughly inspected and repaired as needed by a qualified electrician. I hope it's not the case, but I would not be surprised if there are further issues that need to be addressed, hopefully just simple things like snugging up connections that have worked loose over the years. Your life, your cast and crew's lives, and possibly your audience's lives in case a fire should start are worth any inconvenience it might cause.