An interesting question. Certainly the high level of adventure in this work might lead one to think maybe there is none.
However, we can draw moral lessons in at least two areas from The Count of Monte Cristo. First, we see that there is a limit to human justice. Because of this, we can draw lessons about how humanity should act. We should not reach too far, because we have limits. If we try too much, we will fail and damage others as well as ourselves.
Second, even in the harshest circumstances, the precious elements of the human heart, like love, can survive, and we must act to protect them as the Count did when imprisoned.