Does code permit wire nuts in a sub-panel? I needed to extend a couple wires since I replaced an old panel. If so should I wrap them with tape?

I'm buying a new house, and during the inspection the inspector noticed that the breaker for the A/C unit was too big. It's a 50 amp, and he said it should be 40 amps. The sellers called the company that installed it to have them look at it. They said they do that on purpose for the days in the summer when the unit might be working really hard. That way the breaker won't trip. I guess that makes sense to me, but is that safe? I don't know what the wiring size is, but the inspector commented on another 50 amp breaker that didn't have the proper size wiring, so I'm guessing that the breaker for the A/C has proper wiring.