As mentioned the game seemed to keep continuity where they could (Beauregard tannen for instance was in the first episode of the show which took place during the civil war).
But there's quite a few things from the show which are not true to the characters. As mentioned doc would not authorize using time travel as a way to 'perfect' the past. For instance there's an episode where Marty's ancestor pee wee McFly is a baseball pitcher and they go back in time and give him some enhanced glasses to help him pitch. No way doc would authorize something like that; willingly give technology from the future to a person in the past.