I'm not sure what the doorbell has to do with the rest of your wiring. You can fix the "frying doorbell" by replacing the mechanical strikers (which are prone to burning out in situations like that) with one of the electronic ones.

If you've got copper wiring with grounds and circuit breakers (other than some of the problematic panels like the FPE), there's not anything "different' that rewiring is probably going to do for you other than adding a few additional circuits that used to be allowed to be shared.

You might consider GFCI's in the places they are now required by code if you don't already have them or if sufficiently paranoid putting AFCI breakers on certain circuits.

Completely agree with Ron.
Don't forget to change the buttons as well.

Doorbells and there wiring have very little to do with the other electrical wiring in your house.

The only connection is a single transformer fed by 120 V and stepped down to the low voltage used by the doorbell circuits (18-24 V).

I say "chuck it all" with the ALL being the doorbell wiring. During our remodeling I deleted all the hardwired doorbell wiring and installed a wireless Honeywell doorbell system.

Thanks for the feedback so far...tom in seattle, I think wireless is definitely the way to go doorbell-wise.

To clarify, our doorbell was actually completely on its own, not really connected to anything else, so that itself is not a concern to me, I just got paranoid in general after living with the burnt smell for a while.

I really have to admit to knowing almost nothing about electrical work. Is a house built in the 50's with copper wiring something to be concerned about or is there no real room for improvement? How do you know if your wiring is safe?

I've had housefires on both sides of my family so I am very concerned and uninformed...not good!

ionized,
Thank you that does make me feel better, does old wiring last forever? I mean if all the connections are good? Or does it have a "life expectancy"?

It doesn't help that every rennovation show has "fire hazards" found in the walls, is this common to find or just drama for the show?

"Thank you that does make me feel better, does old wiring last forever?"

Wiring from the 1950s has plastic insulation and should be good almost forever.

Even older wiring may have cloth covered rubber insulation.
It is usually fine unless disturbed.

The rubber has dried out and become brittle, and any movement can cause it to crack, and even fall of the wire in boxes when you do any work in them.

Receptacles can wear out and switches may fail but these devices are easily replaced.

The most significant change sine the 1950s is the running of full size ground conductors on all 15 and 20 amp circuits.

You can use GFCI receptacles to obtain almost the same level of protection if grounds are not present.