Burned Circuit Breakers

It's highly unlikely that the box itself would be a risk for this. It really is not much more than a metal box, with a main breaker and bus bars to attach the circuit breakers. Not much to go wrong there.

If he was a licensed electrician, he would certainly have checked this out when he did the work on it. If you needed additional work done, he would have told you so. Remember that an electrical fire shortly after he has done work in your home is very bad for his reputation. Plus your insurance company might very likely consider suing him, if they think he made an error. So electricians are very careful to make sure it is safe before they leave. I wouldn't worry about it.

But I don't understand your saying that your husband replaced the 'fuses', but then mentioning 'circuit breakers' that the electrician replaced. Do you have both fuses & circuit breakers in your house? That's pretty rare.

He replaced the fuses outside on the A/c unit. We have APOLLO heating inside and a separate A/C unit outside. He just changed the outside fuses.