Continuity mistake: Jack's father the emperor is a young man when he defeats Aku. At the conclusion of the movie, he greets his pregnant young wife. At the start of "The Beginning" movie, Jack is a very young boy, both his parents are well past middle age-and Jack has no sisters or brothers to explain the gap.
Factual error: Even though the show is called "Samurai Jack", Jack isn't really a samurai. The correct title for him would be a Ronin as a Ronin loses their master if their master dies or loses favor with their master and also has no home anywhere. Jack has these attributes. He has no master and no home.