To be specific, we recently had some electrical work done. The electrician added a second panel. He left without labeling anything. So today I've been testing outlets and switches trying to figure out what controls what. I learned that a number of things in the kitchen are controlled by a breaker in both the old panel and one in the new panel. I have zero electrical experience and am wondering if someone can advise as to whether or not this might be okay?
Probably. Here's a diagram of how a main panel and a subpanel are usually wired together:
In this diagram:
So if this behavior matches up with what you are experiencing when flipping breakers, then you're probably OK. Obviously there will be slight differences, such your breakers will probably not be in the same positions in my example, the pair of breakers in your main panel might just be one double-wide breaker, or (unlikely) the pair of breakers in your main panel might just be a single breaker.
But if you're concerned, it is worth it to pay a second electrical contractor to come out and look over the other guy's work. Also, the work should have required permits and therefore an inspection by a government inspector. If that didn't happen, then that might be a red flag.
Also, new electrical work like this must be labeled properly to meet code in most jurisdictions. You are will within your right to call the electrician and insist he properly label his work.