Any party in interest may appeal to the supreme court of the state within ten days after the assessments have been confirmed or passed upon as provided in Section 51-31-49. The record of the proceedings or the bill of exceptions in every case shall be required to be filed within thirty days after the hearing, and the appeal bond shall be filed and approved within ten days after such approval of the assessment. Each party appealing shall execute a separate appeal bond in a sum of not less than $100.00, and a greater penalty shall be required, where in the judgment of the chancellor or court, the costs in the case are likely to exceed the sum of $100.00. After ten days from the approval of the assessments, the decree shall be final as to all persons in interest who have not executed appeal bonds as herein provided or as the court may fix as to the amounts thereof. No appeals shall be allowed in the proceeding until after the assessments are made final by order of the court or chancellor, whether the appeal relates to the assessment or to other features of the proceeding; and no appeal or appeals shall stop the proceedings with reference to the organization and doing the work of the district, but the work and proceedings shall proceed the same as if no appeal or appeals had been had. In case of a reversal in any feature of the proceedings, the errors shall be corrected according to the mandate of the court, so that no injustice shall result from any error of the court first making the error.