Does an error in the wording of the acceptance from the registrar, where he described me as my father's agent instead of the principal, affect the validity of the marriage contract?

The registrar's error in the contract does not affect its validity; for in contracts, what matters are the meanings, not the wordings, and what is considered is the offer and acceptance between the guardian and the agent. So, if the wordings indicate marriage, the contract is valid, because it is validated by anything that indicates its intended meaning.