Continuity mistake: Rex's kama (the black kilt-like thing he wears) is missing twice: first when he, Anakin and Ahsoka are looking at a hologram of an AT-TE on the Resolute's bridge, and second when Anakin's trap for Grievous is revealed, and Rex orders the AT-TEs on the asteroids to fire. (00:01:12 - 00:04:10)
Continuity mistake: At the beginning of the fight with the assassin droids, Anakin cuts off the right arm of the one Ahsoka ends up fighting. Yet during the fight, just before she says "Get back, ya pistonhead", the droid briefly has both arms. (00:12:10)
Continuity mistake: When Ahsoka asks R3-S6 how the droid's first adventure was and Anakin snaps that he thinks he's lucky to be alive, Anakin's clothes below his belt are missing the black overtunic, leaving only the red tunic below it. (00:20:17)
Answer: Dooku never accepted Ventress as his apprentice, as far as I know; he just kept her as his devoted personal assassin. In Phantom Menace, it is stated that there can be only two Sith at a time, to prevent a power struggle in the lower ranks. To accept Ventress as an apprentice, Dooku would have violated that rule.