Continuity mistake: After Grievous has received R3's message, he assures the dismembered R2 that he will not come to harm. We see R2's head lying on the dissection table with his electronic eye dangling from a cable. When Grievous stands up again, just before his MagnaGuards enter, R2 has his eye back in place. It's a brief shot, so you'll have to be quick to catch that glitch.
Continuity mistake: Ahsoka escapes from General Grievous by cutting his right hand off. When Grievous jumps into his starfighter, he suddenly has his hand back. (00:18:11)
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.