The Native Americans living in the area, the Patuxet, were totally wiped out by a series of epidemics between 1616-1619 caught from English fishermen who landed regularly in the area. Luckily for the colonists, they built in the cleared area where the Indian village stood and utilized the cleared farm land that the tribe had abandoned.
Far from being a womanizer, as depicted in the movie, Captain Christopher Jones was a happily-married family man. He and his wife had eight children, one of whom was born in March, 1621, while Jones was still at the Plymouth Colony in Massachusetts, waiting for favorable weather to return home to England on the "Mayflower."
For once, the colonists are correctly shown building framed houses, and not log cabins as is commonly supposed - the latter were introduced by Swedish settlers along the Delaware in 1638, and did not become popular until the eighteenth century.
Dorothy Bradford did indeed fall overboard and was drowned while husband William was exploring for a site for the establishment of Plymouth. Bradford mentions this in his "Of Plymouth Plantation" although the circumstances are not clearly delineated. After the death of Governor John Carver from exhaustion in 1621, Bradford served on and off as Governor for 33 years. Bradford and wife Dorothy did produce a son John, who was born in Holland in 1617. He died childless in 1676 in Connecticut. After Dorothy's death, Bradford remarried.