Continuity mistake: When Count Dooku drops the platform on the unconscious Obi-Wan, Obi-Wan is not lying on the same part of the floor as in the previous shot of him, seen, for example, from the pattern on the floor. Later, when Anakin walks over to him, his position is different again, and the platform has moved as well. He is also lying under a different part of the platform. (00:12:45 - 00:14:30)
Continuity mistake: When Anakin and Padmé are talking on the couch after Anakin is appointed to the Jedi council, they keep changing position between shots, depending on the angle of the camera. The easiest way to see this is to watch the red cloth hanging behind them on the couch. In some shots it is behind Padmé, in other shots, it is behind Anakin.
Continuity mistake: When Obi-Wan and Yoda arrive at the Jedi temple to find all the slain Jedi, there is a wide shot showing Obi-Wan walking several feet ahead of Yoda. Obi-Wan then raises his hands and is about to remove his hood when it cuts and now Yoda is suddenly right next to Obi-Wan. (01:30:40)
Continuity mistake: When Padmé is stroking her son's cheek, as she says, "Oh, Luke." the baby's hands are up by his mouth, which they weren't in the previous and following shots. (02:00:45)