From FAIR, the Foundation for Apologetic Information and Research
Palmyra or Manchester?
Road tax records that indicate Joseph Smith, Sr. was in Palmyra Road District #26 from 1817 until 1822. Since the road tax records were done in April, this indicates that Father Smith arrived in Palmyra after April 1816 and before April 1817.
The first Smith residence was a log cabin, which was inadvertently built off their actual property. Such an accident is entirely possible in a day when boundary lines may not have been well established.
The U.S. Census Bureau listed the Smiths in Farmington (now Manchester) in 1820. The Smith family and most everyone else, considered themselves in Manchester, even though they technically lived about 59 feet off their property.
Moving to Manchester, it seems probable that the Smiths did not formally move to the new frame house on the east side of Stafford Road until after the winter of 1822. This would mean that the Smith family did not actually dwell on the Manchester side of the line until after November of 1822, when according to Mother Smith, “the frame was raised, and all the materials necessary for its [their frame house] speedy completion were procured..”
Correcting the Mistake
An unidentifiable newspaper article on microfilm at Brigham Young University library mentions that after some time, it was discovered that the cabin originally built by the Smiths was not on the land originally contracted by them. Arrangements were then made with Samuel Jennings to purchase the land on which the log cabin was erected.
Finding the Smiths not on their property by just less than 60 feet, the Palmyra road tax overseers recorded the Smiths on their road tax lists until 1822. At this time the Smiths were able to raise the frame of a larger house (this time, on their property), move into the house, and work to complete the house after the move.
This move occurred before the tax liens were completed in 1823. The tax liens on the property increased $300 to reflect the move. The move to the log house by the Smiths in 1818 was considered a move to Manchester by Joseph Jr., in his history, for it was a move to their farm where he was going to labor for many years to come. An imaginary line separated them from physically being in Manchester.
Joseph Smith was living in the area at the right time to be near the Sacred Grove where God and His Son appeared to him. Eyewitnesses, critical of Joseph Smith, do verify that the Smiths were there, where Joseph said they were. Critics now try to claim that he was not there. The evidence proves these new critics wrong.
The full FAIR wiki article may be accessed here. Early Smith family history - FAIRMormon