Deliberate mistake: At the beginning, Asajj Ventress is wearing an outfit with a long skirt. When she is rescued from her damaged starfighter by the scavengers, the skirt has vanished. This was done because the animators found the skirt too difficult to animate. This is also why she receives a brand new outfit that never had a long skirt later in the episode. (00:08:20)
Continuity mistake: When Cad Bane is taken into custody by a clone trooper, the trooper changes from a shock trooper to a standard trooper between shots. (00:14:40)
Other mistake: In one shot after the droid fight in Gha Nachkt's ship, at one point when you see R3-S6 (Goldie), his eye is reversed. (00:12:42)
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: 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: 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)
The Phantom Apprentice - S7-E10
Continuity mistake: During Ahsoka and Maul's duel, just before she kicks him through a wall, he's pushing her down with his double-bladed lightsaber while she's resisting with her two lightsabers. In a shot from behind her, she has one blade on each side of the handle of his lightsaber, but a close-up of her shows both of her blades on the same side. (00:20:19)
Jedi Crash - S1-E13
Continuity mistake: When the Jedi's ship is in danger of crashing into a star while in hyperspace, there is a brief shot where Rex's kama (kilt) is missing, while Ahsoka is arguing with Aayla about shutting down the ship's power. (00:07:05)
Continuity mistake: Pong Krell's goatee is missing during the conversation he has with Rex during the march, most noticeably when he says "CT-7567, are you reading me?" (00:13:25)
Slaves of the Republic - S4-E12
Continuity mistake: When Ahsoka threatens Queen Miraj, she's holding her primary lightsaber. When she's shocked unconscious and falls to the ground, it's her smaller shoto that rolls onto the floor. (00:14:44)
The Citadel - S3-E18
Continuity mistake: When Ahsoka asks Master Plo if she can speak with him, her Padawan braid (the beaded chain hanging on the back of her head below her right horn) is missing. (00:04:05)
Continuity mistake: When Obi-Wan, Waxer and Boil take cover behind some rocks on the way in to Nabat, in a close-up of Obi-Wan, the armour markings of the trooper next to him are missing. (00:04:37)
Continuity mistake: When Mixer and Redeye are first seen patrolling the Coronet's hold, their armour markings are visible in the first shot, but in the second, their armour is suddenly plain. (00:01:42)
Continuity mistake: When Jar Jar and one of the clones are shown burying Kharrus, a creature walking by in the background disappears between the shot where Commander Stone is looking at what's going on and the following close-up. (00:08:53)
Continuity mistake: Ahsoka is wearing a red bodysuit for most of the episode, but when she falls to the floor after Bane shocks her unconscious, her legs are miscoloured a pale pink. (00:13:21)
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: While training Savage, Dooku uses the Force to levitate a number of stone obelisks. While he's doing that, there's a closeup of Savage where an obelisk that is shown floating in the preceding and successive shots is visible behind him not floating. (00:03:36)
Continuity mistake: When the three Jedi Cruisers are shown after a vulture droid crashes into the Resolute's bridge, the one on the left, the Defender, has had one of its two bridges destroyed. After a cut to a different shot, the next shot of the three ships as they turn to retreat has the Defender with both bridges intact. (00:06:28)
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: When Baron Papanoida walks into Jabba's court, his half-cape is missing. (00:10:24)
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.