Right after Kunta Kente is bought by Mr.Reynolds in Episode 2 and Fiddler is about to take Kunta, before the next scene is cutaway, there is a white vehicle passing in front of the gray building in the background, in the back left corner. Automobiles weren't in existence back in the 1700.
The Akan and Kunte Kinte discussed running north to the safety of the abolitionist movement in the supposed late 1700's (according to the story's timeline). The abolitionist movement did not reach crusading proportions until the early 19th century.
When the Slave Doctor is examining Kunta Kinte in Annapolis in 1767, he is singing and humming "Pop Goes the Weasel". The music was written around 1799, and the full lyrics were published in America in 1850.
In Episode 1, a crewman on the ship transporting Kunta Kinte to America in 1767 plays a concertina. The instrument was invented in 1829, and was first marketed with the familiar hexagonal body in 1843.
Much of the topography and flora throughout the series is simply wrong for the areas in which it was set. This is especially true for the Reynolds plantation, located in Spotsylvania County, Virginia, which is shown to be mountainous with a lot of plants native to arid areas (e.g. Southern California). Spotsylvania is neither.
When Kunte Kinte (played by John Amos) met the Akan in the woods, they greeted each other with an Arab-Muslim greeting. The origin and highest concentration of Akan people are located in Ghana. Today, Muslims account for the lowest religious minority in Ghana: 16% of the Ghanan population. It is unlikely the average Akan clan member would have been a Muslim during the time of Kunte Kinte.