Are the breakers the correct type?
The first thing you do is make sure all your breakers are correct for the panel. When people post pictures of their panels, we see A LOT of "alien breakers" where they have brand X panel and someone just slapped in a brand Y "because they fit". They don't fit. They snap in, but the insertion pressure is obviously different and wrong, and they are gripping the busbar in an inefficient and misshapen way, and they will arc and ruin the busbar if they are heavily loaded.
That said, there are "classified" breakers. Siemens QD breakers are 3/4" wide and made (and UL listed) specifically to fit only Square D QO panels - they won't even fit Siemens panels which use 1" wide breakers!
ThreePhaseEel is a subject expert on this, so tap that knowledge!
Are breakers correct for wire size?
Breakers protect wires and devices. Compare the wire size to the breaker size. Any #14 on a 20A breaker? Any #12 on a 30A breaker? Investigate and either downbreaker or rewire.
When homeowners get frequent breaker trips on a circuit due to their own incompetence in overloading it, they often swap in the next size larger breaker simply to stop the trips. This is what we're hunting for.
If you find a dedicated circuit with a motor load with seemingly oversized breaker and undersized wire, shoot a picture of the motor nameplate and come on back and describe the situation to us. There are certain exceptions where this is allowed.
Are Multi-wire branch circuits (MWBC) on 2-pole breakers?
Search for every instance of "two hots and a neutral" -- typically in /3 cable, black red white. Make sure every one of them lands on a 2-pole breaker.
There is a wiring technique called MWBC where two hots share a neutral. That is fine, but it needs to follow extra rules to be safe. It is safety-vital that the breakers be on opposite poles. It's also important that both legs have common maintenance shutoff, so one handle throws them both off for sure. You can slickly solve both problems by feeding the circuit from a 2-pole breaker. (NOT a double-stuff; the handles cannot throw independently!)
There are other ways to do it, but that is the simplest.
Is aluminum wire present?
Aluminum or copper-clad-aluminum wire is special. It has two special needs.
- The wire must be 2 sizes larger (smaller numerically) than copper. That means a 15A breaker needs #12 wire......... A 20A breaker needs #10....... And a 30A breaker needs #8. Make sure that is so.
- Fit AFCI breakers. Back in the day, when aluminum wire was popular, many electricians made very bad choices of terminations - they wired aluminum to receptacles and switches that were rated copper-only, or devices that were hastily rated for aluminum without proper testing. This caused fatigue or dissimilar metal corrosion. Both of these fail by arcing. Arc-fault breakers are a silver bullet.
This used to be a much harder, scarier problem. Thanks, AFCI.
Well, it would be good at some point to follow up and replace old receptacles, switches and splices with CO-ALR (R for Revised) rated devices. Wire nuts should never be used, not even the purple ones; use Alumiconns.
AFCI anywhere else you're worried about.
It really is a silver bullet.