Part 1 Roots: The Saga of An American Family - S1-E1
Other mistake: During the voyage aboard the Lord Ligonier, none of the African captives have shaved nor had haircuts during the long voyage across the sea, but they are clean-shaven and their hair the same length when they berth in Annapolis as when they were first loaded aboard ship in Africa.
Part 1 Roots: The Saga of An American Family - S1-E1
Factual error: The slave ship 'Lord Ligonier' flies the White Ensign. This has always been reserved for the Royal Navy; British merchant ships (as American ships were in 1765) have flown the Red Ensign since 1674.
Part 1 Roots: The Saga of An American Family - S1-E1
Other mistake: Where is the light in Kunte/Toby's slave cabin coming from? There are no candles or lantern, and electricity hadn't been invented yet. Obviously studio lighting.
Part 1 Roots: The Saga of An American Family - S1-E1
Revealing mistake: The young men are all in a lineup, preparing to be circumcised, when the camera pulls back to an obtuse shot of the lineup, whence they're all wearing African drawers. Either for modesty purposes, or purely a filming error.
Revealing mistake: In episode 2, when Kunta Kinte is on the slave ship 'Lord Ligonier', the slaves are trying to take over. During the fight, one of them is going up to a white man and if you look up in the sky you can see a trail from an airplane.