At one point during the film when Rat opens the cash register, the cash register forgets to do it's "ding" noise.
When the Bananas' visit the Teddies house to tell them about the alien rumor, they ring the doorbell. In the next shot outside, the doorbell is missing.
We occasionally see a shelf in the Bananas' bedroom full of games. One of the games is 'Need for Speed: Undercover'. This particular game did not come out until later in 2008.
When Rat loses one of his cereal packets and is looking for it, he knocks a bowl over. We hear the noise of it breaking, but the bowl hit the floor a second earlier than the noise, and the sound it also light, when the bowl hit the floor heavily.
There is one shot during a Rat in a Hat scene in which we see his alarm clock. But when we see it, the ticking sound of the second hand is faster than how the second hand goes on-screen.
When the main villain from the sun (Rog the Alien) puts on his astronaut suit to fly in the local spaceship to Earth. You can see the reflection of the crew on the astronaut helmet. (This is because it is filmed on a studio set instead of animation.)
There is a picture of the Eureka Skydeck on a picture frame early on in the movie. The backdrop of the picture is the city of Sydney(because if you look closely at the backdrop, you can see the Sydney Opera House), when the Eureka Skydeck actually is in Melbourne City.