(at around 3 mins) In the opening montage, Nim is seem swimming underwater with the cloth bandage on her leg she is not supposed to have until she hurts her leg later in the film.
(at around 41 mins) When Alex Rover is trying to convince Alexandra Rover to go outside to the taxi, they show the door is latched. In the next scene Alex Rover walks over to the door and the latch is undone.
When Nim goes underwater in the storm, it is clear to see in one shot she is wearing goggles.
the bandage starts off on Nim's left leg then on at least one occasion moves to her right leg.
The depiction of Rarotonga as a primitive "native" island is very patronising. It is far more developed than that - the airport can even take jumbo jets. Also, they would never give coconuts to arriving tourists - they are considered so mundane, that they are used as pig food.
The captain of the cruise ship wears captain stripes on the sleeves of his jacket but lieutenant commander epaulets on his shoulders.
When Nim was trying to reach Jack after a big storm, the satellite is shown to be working properly underwater despite having it being detached from the phone.
(at around 22 mins) After the storm, Nim discovers there's power so she re-connects the solar panels. But when she goes back and turns on her computer, it re-boots to exactly the same page as it was last time which is not possible.
Alex takes a small plane to Rarotonga. The island of Rarotonga has an airport that can land a 747. There are direct flights from Hawaii and New Zealand. The only small airplane flights are to/from smaller neighboring islands.
It is unlikely that the small plane Alex took could have reached Rarotonga, as it would be too long a flight from Borneo.
(at around 47 mins) When Alexandra rushes at Borneo airport, there is a sign written "Jogja Tourism". Actually, Jogja (Yogyakarta) is in the island of Java, not Borneo.
Alexandra Rover (Jodie Foster) is flying from San Francisco to Raratonga (Cook Islands) via Borneo (Kalimantan in Indonesia). It is very unlikely to happen because between San Francisco and Borneo the airplane will have well passed the Cook Islands. The nearest international airport that may take her to Cook Islands is Nadi in Fiji (South Pacific) and from there can fly to Cook Islands via Air Pacific.
Borneo is in the South Asia region. So it is crazy enough to transit in Asia while the destination is in the South Pacific island.
(at around 13 mins) There is no such thing as a "Southern Borealis". That is an oxymoron as Borealis means Northern. They probably mean Aurora Australis. This mistake is corrected in the Spanish dubbing of the film.
(at around 55 mins) The characters refer to a tropical storm as a "Monsoon" when they should be calling it a "Typhoon" (or more accurately, as they are in the South Pacific, a "Cyclone").
As Alexandra was reading the first email Nim sent, it wrote "Dear Alex Rover, I'm sure Jack would love to help you with your newest adventure. He'll be back on Thursday. He's a great fan of yours. We both are. From Nim." Nim didn't write the back on Thursday part.