In the scene where 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.
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.
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.
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.