Continuity mistake: When R2-D2 closes the door to the platform in the back of the monastery (before Asajj attacks Ahsoka), Asajj stabs both of her lightsabers through the door, a few inches apart from each other, and starts moving them downward. In the next shot, on the other side of the door, there is already a solid line (the top of the circle) cut into the door. There wasn't enough time for her to have stopped and connected the space between the two holes.
Continuity mistake: When Asajj is reporting to Dooku and she tells him to wait (before Obi-wan shows up), you can see in the hologram that she ignites both of her lightsabers and turns around. However, in the next scene (at her location), there is no sign of a hologram transmitter/projector, which she would have been using to talk to Dooku. There is just a door and some battle droids in front of her. Even if she was using the handheld device that is shown earlier in the movie, there wasn't enough time for her to have put it away and gotten her lightsabers out, since Dooku's point of view shows her already turning toward Obi-wan.
Continuity mistake: When Ahsoka and Anakin are using the box to sneak through the droid army, Ahsoka eventually stands up. The shot shows the road ahead of them is completely empty. However, in the next shot, they are walking under the box and they run straight into a destroyer droid.