In the scene where Nicholas is helping Mia with her archery, right after he says the line "Can I see you one more time before I go?" His lips appear to still be moving though Mia's voice is heard answering his question. There was most likely different dialog there.
In the "Dancing footman" scene, it cuts back to the interior of the room the footman is dancing outside of. The same footman is standing directly behind the Queen. Then it cuts back to the dancing footman in the hallway.
In the scenes where Mia is reviewing the troops, there is a shot where Lily and Nicholas introduce themselves across Andrew ("Best friend of the queen-to-be. I don't like you.") In a later, related scene, Nicholas has followed Mia to the tack room. His necktie changes between the two shots. The director says (in the special features part of the DVD) that this was actually a shot taken from another scene: the pear tree scene (which is in the deleted scenes), and put into this scene instead.
Before Mia and Nicholas fall into the fountain, Mia is holding her fan. When she comes out of the fountain, there is no fan in her hand nor in the fountain. The fan would float if she had dropped it while falling.
When Mia sees her apartment inside the palace for the first time, the view out of the windows show they are on the ground floor. Later in the movie when she climbs out of the window to meet Nicholas, she climbs down the trellis from the second floor.
At Mia's slumber party during the singing, Mia is sitting on a chair that is festooned with lace and other bridal type stuff in the front side shots. In the behind shots the chair is plain. It should be showing at the back because of the way the piece of lace especially is draped over the chair.
When Lily comes out of the closet in Mia's new room, they are standing in front of the open closet. They cut to the Queen. When they come back, Lily and Mia are now standing in front of a flower arrangement.
Toward the beginning of the film, Mia is standing in the throne room, surrounded by a gallery of portraits of rulers of Genovia. At one point, toward the back of the hall, a famous state portrait of Martha Washington can be seen on the wall of Genovian royalty.
Lady Elyssa is said to have won a Rhodes scholarship, but the Rhodes scholarships are only for citizens of American and Commonwealth countries -- British nationals are not eligible -- to study in England, and none of the nations eligible to send students have hereditary nobility.
In the beginning of the movie (at about 00:01:49) the princess is leafing through her diaries. On one page you can see a 20 EURO bill taped to the paper. It's a counterfeited bill, or better a kind of fantasy-bill, composed of parts of the real bill.
At the wedding, when Mia addresses the members of parliament, saying why she wants to rule without a husband and why she would be a great queen, her friends from America are shown watching her live on TV. However, there is clearly no camera crew inside the church where the wedding takes place, and nothing suggests the event is being broadcast.
In the scene where Paolo is arranging Princess Mia's hair for the wedding, he states that he is Italian, that "all Italian men love babies." In the same scene, just before revealing Mia's last hairstyle, he counts off, "Un, deux, trois." This is French, not Italian, Paolo may be Italian but that does not mean he can't speak french.