This will bring about a great deal of discussion.  I would say that the issue of moral responsibility is of the most significant point in the novel.  The question that strikes at much of the development of the novel is the idea of how much individuals have to assume for their creative powers.  Frankenstein's pursuit of science to new ends, frontiers not yet established or articulated, help to create something terrible and responsible for a great deal of damage.  Rather than acknowledging his role in this creation, Victor runs away and abandons his creation.  In the end, the question in my mind becomes how responsible is the monster for what he does and how responsible is Victor for creating it.   I do acknowledge that towards the end, Victor becomes driven to destroy it and does assert some moral responsibility, but in the act of creation and when consequences were not envisioned, how responsible are individuals for the results of such endeavors become the critical issue in my mind of the novel.

Mary Shelley's Frankenstein poses existential questions about the identity of man, his relationship with God, his role in the natural world, and the roles of language and morality.

Identity: Who are we?  What makes us human, God-like, and monstrous?  Who are our allegiances to: our parents, God, or ourselves?

Relationship to God: Are we born into sin?  Has God abandoned us?  Can we ever really know our Heavenly Father?  Should doctors and scientists play God?

Nature: Is nature knowable, insensate, or evil?  Can we use it for the betterment of mankind?  Should doctors and scientists tamper with nature?  Is nature at our disposal, or should we protect it for the future?

Language: Is language acquisition the key to separating us from monsters?  Does it lead us to knowledge or destruction?  Is it better to express our pain with words or suffer silently?

Morality: Is personal revenge wrong?  What mistakes lead to tragedy?  Are we bound to extending life by any means necessary, or should we let nature run its course?

To me, what is most significant in this book is the theme of the danger of too much scientific knowledge.  When Mary Shelley wrote this book, it was the Romantic era and people were distrustful of science.  But I would argue that you can say that this message is just as relevant today.

Today, we see science seeming to go places it has never gone before.  We have the possibility of cloning and gene therapy and other techniques that have never been possible before.  We also have terribly destructive technologies such as (potentially) biological weapons.  This makes it seem that maybe we should pay attention to the message of this book.