Continuity mistake: For one shot near the start, the lightsabers on Ventress' belt are behind the buckle, but in all other scenes, they are hung in front of it. (00:03:56 - 00:04:38)
Continuity mistake: After the droid advance force has split up to hunt down Master Yoda, the Jedi Master and his clone escorts attack each group on their own. When Yoda ambushes his group, it has six battle droids; but he is seen finishing only four of them. The remaining two just vanish from the scene. (00:10:10)
Continuity mistake: After Yoda cuts a hole in one of the droid battle vehicles, and throws the droid out, the following scene returns to Asajj and the Toydarian king. When their backs are shown, Asajj is standing close beside the king, but in the very next shot (showing them from the front), she is obviously a few feet farther from him. (00:17:08)
Continuity mistake: Wolffe, Sinker and Boost are shown boarding the escape pod twice: first from inside of it and then in the next shot from the pod bay running past Master Plo. (00:03:35)
Continuity mistake: When Plo Koon asks Matchstick about the damage to his Y-wing, Matchstick is wearing the standard Shadow Squadron helmet instead of his custom-painted one when he responds. (00:14:25)
Continuity mistake: When Obi-Wan Force-pushes the second droideka in the hyperdrive room, it rolls a considerable distance down the catwalk before striking an approaching squad of droids. However, in a following shot from below, the collision is much closer to where Obi-Wan was standing. (00:15:03)
Continuity mistake: When Obi-Wan says, "Unlike you, maybe he's getting some much-needed rest," he's stroking his chin with his hand. Mid-sentence, the scene cuts to a closer shot of Obi-Wan, and his hand changes position. (00:02:50)
Continuity mistake: When Rex pulls off the helmet of the disguised commando droid, Cody is missing the piece of armour protecting his right thigh. (00:09:37)
Continuity mistake: Before the clones retake the base, they have just enough blasters between them for all five of them to wield one each. When Rex is dealing with the commando droid captain, his left holster still has a pistol in it even though he loaned his other pistol to Cody. (00:14:00)
Continuity mistake: When Rex starts giving the rookies a pep talk, as well as in the shot afterwards where all the clones grab their helmets, Echo's helmet is missing the binocular attachment. (00:16:28)
Continuity mistake: When Grievous calls a battle droid who asks if the Rishi station's destruction was a good thing an idiot, the clasp of his cloak is missing. (00:21:15)
Continuity mistake: During the end scene, when Echo and Fives are honored for their services, in the first shot, Echo's helmet is missing, despite his arm being positioned as if he's holding it. When his helmet appears, it's missing the red binocular attachment, which only appears later in the scene. (00:22:00)
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)
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)
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: During Dooku's conversation with Sidious, he's wearing his cape. When Dooku stands up as Ventress enters the room afterwards, his cape has abruptly disappeared.
Continuity mistake: At the beginning of the briefing about the visit to Florrum, Rex's kama (kilt) is missing. (00:15:49)
Continuity mistake: When Obi-Wan and Anakin snap "YES!" in response to Dooku's question, Obi-Wan's hands, cuffed together with a pair of handcuffs linked by an electrified cable, have somehow moved so the cable on his waist chain is inside the circle of his arms, despite that not being the case when he came to inside the cell earlier in the scene. (00:01:36)
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.