When Dave drops the pair of mittens, Theodor has a sandwich in his hand. He picks up the mittens and calls, "Don't forget your mittens Dave; it's cold in Europe." But he clearly hands Dave the sandwich instead, and is about to take a bite out of the mittens, and then in in the next shot, Dave suddenly has the mittens.
When the Chipettes are about to go scuba diving Eleanor's eye color changes from blue to brown.
When Simon is about to drop a doll down a "pipe" in Venice, it is an Alvin doll. In the next shot it is a Simon doll.
When Jeannette picks up the Chipette doll that is filled with diamonds, it alternates between being a Brittany doll and an Eleanor doll.
While singing "Rock 'n' Roll" the Chipettes walk up some steps, and the Chipmunks do the same. Viewed from the front of the Chipmunks, the Chipmunks walk up the step in this order, from left to right: Simon, Alvin, Theodore. In the next shot, Simon and Theodore switch places.
During the Off to See the World song, the boys are shown in a gondola. Simon is standing at the front, clearly holding on to a red Alvin doll. But when they reach the pole seconds later, Simon lifts the top and throws in a blue Simon doll.
During the song "The Girls of Rock and Roll," when the Chipettes sing the line "The things they're trying to sell us," their lips aren't moving at all. The same thing happens again later in the song when the Chipmunks sing the line "We'll never stop believing" without moving their lips.
In Greece, the Chipmunks and Chipettes are surprised to see each other, yet they parked their balloons at the same spot. Even if one group arrived after the other, that group would have seen the balloon and known the others were already there.
When the Chipmunks are in their bedroom getting ready to call Dave, we see Simon reading a book. When he turns a page he turns it to the right as if he was reading the book backwards.