The exterior shots of the airplane the family takes to Hawaii is a MD80 however the interior shots of the plane are of a wide body jumbo jet. Furthermore, the MD80 has never been ETOPS certified, which is required for a mainland to HI flight.
When Jan, Peter, and Bobby are talking in the bathroom she hangs the towel on her headset but in the wider reveal, especially noticeable in the mirror, she re-hangs the towel and her hand bounces around.
At the pool Marcia is listening to the 8-track of Davy Jones' solo album on the tape player and the song "Girl" is playing. That song does not appear on the album.
At the start of the movie, Carol's first husband and his partner unearth "the lost horse of the first Tang emperor" somewhere in Krabi province, southern Thailand. While it is true that the tomb of the first Tang emperor, Gaozu (a.k.a. Li Yuan), has been lost to history, it certainly wasn't located in Thailand, but most probably in the heartland of the Tang dynasty, the Shaanxi province of central China.
Police cars on O'ahu (Honolulu) are not black and white with red & blue lights, they are white with a blue stripe down the center and they have a blue strobe lightbar.
When Roy eats the spaghetti with the psychedelic mushrooms in it he appears to have the "munchies," with a voracious appetite. In reality, psychedelic mushrooms suppress appetite and often cause nausea to those who ingest them.
The pamphlet with the adult number that Jan calls to pretend its George has the phone number 555-HUNK written on it. She is seen dialing the number "1" 3 times which does not correspond to the last 3 letters in HUNK (UNK).
When the family discovers Carol's shoe print, the moving shadow of a crew person is briefly visible in the lower left corner of the screen.
When Greg and Marcia suspect that if Roy is really Carol's husband, then they're not really brother and sister, despite the fact that it's been completely obvious that they were in no way biologically related anyway. This is, however, an obvious nod to the fact that Barry Williams and Maureen McCormick dated behind the scenes of the original series.