When any part of a city of the first class, city of the second class, or village shall have been platted (1) the plat having been recorded with the register of deeds of the proper county for more than ten years; (2) the streets and alleys having been dedicated to the public and such city or village having accepted such dedication by maintenance and use of such streets and alleys, and the inhabitants of that part of such city or village having been subject to taxation including the levy of such city or village and having had the right of franchise in all the elections of such city or village for a period of more than ten years; and (3) such part of such city or village is contiguous and adjacent to such corporate city or village or a properly annexed addition thereto; but, when there is error in the platting thereof or the proceeding to annex the part of such city or village which renders the annexation ineffectual or where there is a total lack of an attempted annexation of record, the city council or village board of trustees of such city or village may by resolution correct the corporate limits, if adopted by a two-thirds vote of all members of such city council or village board of trustees. The resolution shall describe the part of such city or village in general terms and direct the proper officers of the city or village to make application to the district court of the county in which such territory lies for the correction and reestablishment of the corporate limits of such city or village. The resolution, and the vote thereon, shall be recorded in the minutes of the city council or village board of trustees.