Continuity mistake: When Anakin and Padme kiss in the alleyway, an alien passes by, glancing at them, and they break up. But in the first shot (from the main street side), when the alien looks at them it is almost past the alleyway. But in the next shot, when Anakin and Padme break apart, the same alien starts walking by the opening once again.
Audio problem: When the Jedi Council are discussing Anakin's promotion to Jedi Knight, in a wide shot, we hear the voice of the female, dark-skinned Jedi saying, "Yes. We need more knights." But her mouth is closed as she says this, and the male Jedi Even Piell (the Jedi talking in the previous shot) is moving his mouth as if he's the one talking.