One moral lesson from Frankenstein is that you are responsible for the lives you create, even if you don't like the way they turn out.
The swath of death and destruction that the angry creature wreaks on Frankenstein's family and friends is the result of his rejection by his creator. Victor was his parent, even if he made his "child" out of body parts, yet he fled his child in horror, leaving him to fend for himself. Although in telling his story, Victor goes on at length about how he benefitted from a loving family, he doesn't seem to have the empathy or maturity to extend that love to a needy child of his own. As the creature explains to Victor,
I do know that for the sympathy of one living being, I would make peace with all. I have love in me the likes of which you can scarcely imagine and rage the likes of which you would not believe.
If Victor would only have offered love to his creation, so much rage and violence could have been averted.
Another moral lesson is that Victor—and the other people who encountered the creature—should have looked past his hideous appearance to try to find the good soul inside. Shelley makes the point that humans are more than our outward appearances. Yet the creature is judged by those who encounter him as an evil monster solely on the basis of his looks, without these people making any attempt to enter into relationship with him.
Finally, as the subtitle of the novel suggests, by calling Victor the modern Prometheus, too much personal ambition can lead to terrible outcomes. Victor overstepped his bounds in creating human life out of inanimate matter, if only because he wasn't emotionally ready to deal with the consequences. Shelley suggests that we should think through the actions we take, especially if they are ego based, before they cause great harm.