(1) Hear and decide appeals where it is alleged there is error in any order, requirement, decision or determination made by an administrative official in the enforcement of this chapter or of any ordinance adopted pursuant thereto;

(2) Hear and decide special exceptions to the terms of the ordinance upon which the board is required to pass under such ordinance;

(3) Authorize, in specific cases, such variance from any zoning ordinance, code or regulation that will not be contrary to the public interest, where, owing to special conditions or exceptional situations, a literal interpretation of any zoning ordinances, code or regulation will result in unnecessary hardship or exceptional practical difficulties to the owner of property so that the spirit of the ordinance, code or regulation shall be observed and substantial justice done, provided such relief may be granted without substantial detriment to the public good and without substantially impairing the intent and purpose of any zoning ordinance, code, regulation or map; provided, however, that notwithstanding any provision of law to the contrary, the legislative body of any city or incorporated town may, by ordinance, vest a designated town official or department with authority to administratively grant a dimensional variance for existing conditions that do not exceed 1 foot of the required dimension restrictions without the application being considered by the board of adjustment, subject to the standards, procedures and conditions set forth in the ordinance granting such authority.