Often I'll identify a wrong value, or bad object, and then search for that through the logs to see what is touching it or where it first appeared. If it's interacting with another value I'll search for that, maybe in a longer chain. Eventually you figure out where the interaction is going wrong, and more often than not it's a subtle error that looks right but isn't. You make a small change (the classic is an off-by-one error) and suddenly everything works perfectly.