Episode II - The Samurai Called Jack - S1-E2
Revealing mistake: When Jack cuts the flying car's hood off, he slashes it vertically, but it is cut horizontally.
Episode XXVII - Chicken Jack - S3-E1
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.
Episode XX - Jack and the Monks - S2-E7
Revealing mistake: Immediately after the time portal is destroyed, it stops raining but there is no moisture anywhere.
Episode XXVI - Jack's Shoes - S2-E13
Continuity mistake: When Jack meets the old father, watch the platform thing he is on. The yellow/black pattern alternates on the right side.
II (The Samurai called Jack) - S1-E2
Continuity mistake: Right before the three-eyed waitress leaves to talk to Aku, there is a shot of an octopus-like bartender, whose facial expression changes in each shot.
Episode XCII - S5-E1
Deliberate mistake: Jack stops his motorbike beside a stream, and Jack's weapon strap crosses over his left shoulder when he walks over to have a drink. The problem is when we see Jack's reflection in the water, his image is not reversed; note the strap is still crossing over Jack's left shoulder. (00:07:20)
Episode XXIX - Couple on a Train - S3-E3
Continuity mistake: On the train, Josephine walks past Jack when he's given his cup of tea. In this shot of Josephine, her facial beauty mark is on her left cheek, but in previous and following shots her beauty mark is on her right cheek. (00:07:35)
Episode XXIX - Couple on a Train - S3-E3
Continuity mistake: After Jack releases the train's log load, it thwarts Ezekiel temporarily. When Jack enters the coach car and takes his seat, it then cuts to an exterior shot of the speeding train's passengers as it passes the windows, and Josephine's beauty mark is missing from her right cheek, though we should absolutely see it in this shot. (00:13:00)
Episode XXIX - Couple on a Train - S3-E3
Continuity mistake: When the train leaves the station, it begins the journey with three coach cars, but as the train speeds along the number of coach cars continues to increase. Then, by the time Jack defeats the Clench duo, the train's coach cars have multiplied significantly, to well over twenty. (00:06:20)
Episode XXIX - Couple on a Train - S3-E3
Continuity mistake: When Josephine grabs Ezekiel by his poncho, she is wearing a black glove on her right arm, but when the scene cuts to Ezekiel when he says, "What business is it of yours?", the glove disappears, showing Josephine's arm bare, but in the next shot, she is wearing both gloves again. (00:08:40)
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.
Suggested correction: Nor is his name really Jack. "Jack", and thus "Samurai Jack", is just an alias that the prince takes. It's not meant to be his title or rank. Just like Cowboy Jack wasn't actually a cowboy.