In the beginning of the movie, during the first performance of 'Real in Rio' the yellow Macaw that baby Blu looks to has three chicks. She only throws two out of the nest then flies away with the newly flying chicks, leaving the third one in the nest.
When the bird sanctuary guard rips off his clothes and begins dancing, his wrists are bare, but when he is giving his report to the police officer, he has fluffy straps around his wrists, matching the ones he has on his ankles.
When Blu is standing on the makeshift light runway preparing an attempt to fly, the section of wire at the end of the runway is shown draped and absent of lights, but as he runs the wire changes, it is no longer draped and has no gap in the lights.
Standard Brazilian license plates are light gray with black letters. They are composed by three letters followed by four letters (i.e. ABC-1234) as opposed to the three letters/three numbers shown in the movie.
Sulphur crested cockatoos are native only to Australia an neighboring islands, and there is no similar South American species. However Nigel is a house pet and it is plausible that the smugglers have operated in other continents.