In numerous scenes with real actors, the boom mike is clearly visible over their heads, occasionally with various covers and moving from one actor to the other. Moreover, sometimes even the boom itself is visible in the top right-hand side corner of the screen.
(at around 3 mins) When the chipettes are singing "Trouble" there are two little girls in blue shirts behind them. After Alvin arrives, the girl on the left is wearing a white shirt and her wristband is on the other arm.
(at around 52 mins) What Alvin refers to as a honey badger is in fact a meerkat, neither of which are native to the South Pacific. Meerkats are native to sub-Saharan Africa, while honey badgers are native to Africa, the Middle East, and the Indian subcontinent.
When Simon takes on a French personality he calls himself Simone. If he were French, his name would not change to Simone unless his personality were also female, which it's not. Simone is the female French form of Simon. Simon in French is spelled the same as it is in English, but pronounced see-MAWn. Simone, on the other hand, is said see-MON like it is said in the movie,
(at around 23 mins) When Ian and Dave are floating in the ocean, Ian clearly has an opening in the suit where his neck is. Water is clearly floating towards the opening, so it would be impossible for the suit to float.