Continuity: It's made clear that Danny Morgan and Trudy are unmarried. Yet when Sandy interviews her on the disappearance she's listed as being Trudi Morgan. She would only have Danny's last name if they had gotten married.
Continuity: At the end of the film when Danny and Glenda float away, their deckchairs move, but the shadows that those deckchairs cast remain in place.
Continuity: When Glenda puts on her helmet to get on the motorcycle she doesn't properly thread the strap, yet at the next stop her helmet is properly adjusted.
Continuity: When Danny leaves the house the morning after spending his first intimate night with Glenda, he has no shoes on. Yet in the subsequent shots (as he meets with a gaggle of reporters), Danny clearly has black shoes on.
Continuity: When Danny first falls out of the tree in Glenda's yard he has a large cut on his shoulder, which Glenda helps him clean. It's still there the next morning when he swims in the river, but by the next time we catch a glimpse of his shoulder, just a few days later, it's gone.
Revealing mistakes: When Danny bites the balloon and falls out of the chair, the next shot shows the AMP Building (viewed from above) in a mirror image.
Factual errors: When Danny encounters the fireworks, his balloons filled with helium would not have exploded, given that helium is an inert gas.