Any person affected by or having any objection to the assessment provided for in section 34-9 or any of the proceedings thereto, may appeal to the City Council. An appeal shall be effected by filing with the City Clerk, prior to the day fixed for the hearing upon the assessment, a written notice briefly specifying the grounds of appeal. At the time fixed for the hearing upon the assessment, the City Council shall consider the assessment and hear and pass upon all appeals respecting the same or proceedings thereto and may remedy and correct any error, irregularity, defect or informality in the proceedings and may make any order which it shall deem just and proper. When no appeal is taken or when the orders and determinations of the City Council upon appeal have been complied with and the City Council is satisfied with the correctness and legality of the assessment, it shall by resolution confirm the assessment and its judgment therein shall be final and conclusive upon all persons entitled to appeal under the provisions of this section, and as to all errors, defects, irregularities and informalities not directly affecting the jurisdiction of the City Council to order the planting, care and maintenance. (Code 1962, § 35-32)