grab a multimeter and figure out what the normal operation of the switch is. it's probably 12 or 24 vdc. leave the multimeter hooked up and watch it while the system is off, operating normally, and experiencing the problem. the resistor is probably a supervision resistor, so there are at least 3 possible outputs from the switch: open, resistor load, closed/short.
you can then decide the best way to diagnose the problem.
once you know how it should be operating, you can, for example, remove the switch and short or open or use the resistor to trick the furnace in to thinking it is still hot and the fan needs to keep running. if the fan doesn't run properly, then you know the problem is not the limit switch.
If you are the landlord I would have another electrician come out to check it. It be something like a factory defect in the subpanel or main panel. Every lug could be tightened and torqued to factory specs but the lug might be stripped out.
If you are the renter then I would make it clear to your landlord that this is a serious problem and you want if fixed now.
Which ever you are I would have every lug on the ground, neutral and hot sides torqued down to factory specs. Get the electrician to do a thermal reading while the panel is hot and having the problem. This would surely cause extra heat where ever it is happening. If the electrician does that and nothing changes have PGE torque everything on their end and do the thermal reading.
I had the same problem and when they removed the meter and left I removed the Edison side covers and one of the lugs was never tightened on their end but it was a factory connection that was the problem.
Edit On questions on what to use to torque a circuit breaker, see this. Each breaker has a label on it with the torque rating on it. At one time there was talk of inspectors carrying torque wrenches with them to spot check circuit breakers, but I know of no electricians own a torque wrench. When I ask they say just tighten them down as hard as you can and they will pass any test. My guess is that most residential breakers use about 20 to 25 foot inch lbs per square inch.
Most of the time torquing happens is in industrial plants where they want to get the maximum life out of everything, including breakers. This is also why thermal cameras are sold to electricians. Heat spots are bad and most of the time it is a loose connection.
In the OP's case I would definitely use the phrase Torque to specifications, especially if he puts any thing in writing. His problem can wreak havoc on electronics and motors.
Best Answer
If you've replaced most of your lightbulbs with CFL or LED bulbs, they present a more inductive load to your power line than incandescent bulbs. This inductance, usually caused by a power converter inside the bulb, doesn't like it when the switch opens.
This inductance will actually force current through the switch as it opens, causing a much larger arc than would normally be expected from incandescent bulbs.
You'll also see this on circuits using 12V lighting (some track lighting and other specialized lighting).
The arcing is safely contained inside the switch, but it will wear the switch down over time, presenting a greater resistance in the power path and heating up. While it will never pose a fire hazard (as long as it's UL rated or similar) it may eventually fail.
If you want to avoid the noise associated with the arcing, get a dimmer that is compatible with all the lamps on the circuit and make sure they are dimmable. The dimmer switches the load electronically, and even if you never use the dimming feature the arcing will not occur. However, the same issues are still present and dimmers under these circumstances will wear out more quickly and fail just as the switches would.
You could also replace the lamps and lamp styles to reduce the arcing. Remove all the lamps, check to make sure there's no arcing (if there is, there are other loads you need to remove, or you have low voltage lighting) and then put each lamp in one by one, testing between each lamp. You may find that it takes a certain number of lamps (in which case a 20 amp switch might resolve the problem, even though the circuit may only be 15 amps), or certain types or styles of lightbulbs or lamps are the problem.