When Nigel is recruiting the Marmosets for help, he threatens three monkeys after he tosses the main one in the sky. One monkey has his hands over his eyes, another over his ears, and another over his mouth. (See No Evil, Hear No Evil, Speak No Evil).
Director Carlos Saldanha (himself a resident of Rio) first came up with the concept in 1995. Originally, it was about a penguin washing up on the beaches of the Brazilian city, but when he learned of the production of two penguin-related animation features - Happy Feet (2006) and Surf's Up (2007) - he was forced to radically re-write his screenplay.
During production, Jesse Eisenberg was still working on The Social Network (2010). To compensate for time, he agreed to provide Blu's dialogue on weekends, admitting that it diverted him away from the mindset of his nearly-joyless Social Network character.
Right before Blu and Jewel's escape from the smugglers hideout, it is possible to see that the soccer game on television is a match between traditional rivals Brazil and Argentina. This plausibly explains why everybody seems to be so obsessed in following the game - especially because the movie seems to indicate that the match is being held in the Maracanã Stadium, in Rio De Janeiro.
When Blu tells Jewel to check his math to verify that his plan to break their chain will work, a patch of sand is shown where Blu has scratched in the equation "f=G (m1 x m2 / R^2)". This is the formula for calculating the gravitational attraction between two bodies and can apply both literally to the rock and chain/Earth, as well as figuratively to Blu and Jewel.
The film lost out at the Academy Awards for Best Original Song to The Muppets (2011). This was the first time only two songs were nominated in the category, instead of the usual three or five. This lack of nominees in this particular category attracted widespread criticism, and led to a full slate of five nominees the following year.
This film, along with Ice Age (2002), Horton Hears a Who! (2008), and Ice Age: Dawn of the Dinosaurs (2009) are the only four Blue Sky films to be nominated for the Saturn Award for Best Animated Film. What they all also have in common is that none of them won. Ice Age lost to Spirited Away (2002) (This was also the case at the 75th Academy Awards), Horton Hears a Who! lost to WALL-E (2008), Ice Age: Dawn of the Dinosaurs lost to Monsters Vs. Aliens (2009), and this film lost to Puss In Boots (2011).
The movie was said to have been the reason for Disney and Pixar's "Newt" project, which had the same plot of having the lead character, who is of a rare species, having to mate with the female of his kind. John Lassetter, one of Pixar's senior heads, hinted, although not explicitly stated, that this was the case.
The trivia items below may give away important plot points.
When Tulio dresses as a Blue Macaw, he looks himself in a mirror and says "Cyanopsitta Spixii", referring at the species Blu and Jewel belong. Cyanopsitta Spixii actually is a critically endangered bird, and its looks are a lot like Jewel. There are only seventy specimens kept in zoos and ornithological collections.
The movie has several elements similar to Happy Feet (2006) (for example, both feature singing and dancing birds, the movie ending with the main male and female characters' offspring being seen, and some rude humor early on).