Both my dentist and I prefer mediation. Am I better off with Arbitration or a Lawsuit to guarantee collection?

If you have a binding agreement for arbitration or mediation (which are different procedures) but your dentist never signed it, you might not be bound if he isn't. And in that case, civil litigation for medical/dental malpractice and breach of contract may be an option.

Nothing guarantees collection, since getting a judgment and collecting it are two different things.

If you make any kind of claim against this dentist, he'll probably submit it to his malpractice insurer, if he's got one. They could a settle with you or hire a lawyer to fight it.

It sounds like you think you have a claims for negligence (malpractic, work performed below the standard of care) , and breach of oral contract for the refund. Depending on the type of liablity and amount of damages, you're probably best off, if you can find a med mal lawyer to take your case, is to sue in court, as juries are known to be more generous than arbitrators and mediators, and the dentist will be concerned about the negative publicity.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.