The series proceeds from the strongest claim to the weakest under the common law. There is an almost absolute right to recover an amount paid on a judgment. There is an almost equally strong right to recover a current property tax payment if ownership is lost. There is a very strong right to recover a disputed tax payment but it is not absolute. In the Third Restatement, the right to recover for contractual performance rendered in a dispute is qualified by a threshold requirement that the performance avoid a loss. Under the Third Restatement there is no right to recover for an improvement to property made with the knowledge that ownership is disputed.

None of this has anything to do with mistake. You could say the payment is recoverable because of failure of basis but that doesn't explain why sometimes the claim is denied.