Continuity mistake: When Princess Mia goes to hold her baby brother Trevor, her mom has him wrapped up with the covers over his head; we can't see his head. When Princess Mia takes him from her mother his head is still covered. But in the next shot, as she turns around toward the camera, his head is uncovered and has a white knit cap on it. But then after they take a few steps and her mother talks to her, his head is covered back up.
Continuity mistake: When Princess Mia is climbing down "vine" to meet Nicholas, we see SG Lionel and SG Shades playing chess with a monitor showing video feeds from security cameras. The one that shows Princess Mia has her higher than the window she is supposed to be climbing out of (there isn't one higher), the window isn't open like it showed in previous shots and she has on a huge white garment of some type that is past her feet (Princess Mia's sweater is gray and comes to her knees). Obviously, the picture we see on the security guards' monitor is not the same one that Princess Mia is shown to have climbed out.
Continuity mistake: During the parade, Joe in seen riding on the back of the carriage that Queen Clarisse and Princess Mia are riding in. When Princess Mia stops the carriage, Joe gets off the back and is down on the street. We see several shots of Joe down on the pavement watching Princess Mia as she is talking to the orphans. As Princess Mia is telling them how to be a princess, you can see Joe in the background and he is up on the back of the carriage again. As the drum roll is announced, we see Joe get back up on the carriage, again.
Continuity mistake: In the scene where Nicholas is telling his uncle that he was wrong, that Princess Mia has found a suitable husband within a week, the scene shows Viscount Mabrey pulling down his vest and then adjusting his tie with his left hand. His hand is still up on his tie when the shot switches to Nicholas saying, "a husband within a week." The shot switches immediately back to Mabrey and his left hand is down to his side and not even visible. Don't think he could be in that pose so quickly.
Continuity mistake: When Princess Mia is seeing her suite for the first time, we see her "closet" and in the middle is a red/orange tufted ottoman that has nothing on it. There is a second shot of the ottoman and there is nothing on it. But then we see Fat Louie on the ottoman pressing a second remote to open/close drawers.
Continuity mistake: When Mia is with that prince using arrows, her elbow is way high up. When the prince runs his hand over her arm, it is straight, then in the next shot it is high up again.
Continuity mistake: When Mia's mother is in her closet, she stands up and hands Mia her little brother. In one shot Mia is supporting the baby's head with her right hand, the next shot with her left hand, then back again.
Answer: My guess is because Mia and Michael didn't actually start dating until the third Princess Diaries book. The second and third books were all about Mia trying to get Michael to go out with her, and since they went out at the end of the first movie, they couldn't base the second movie on the second book.