When Cody and Stephanie hear the baby cry from the tower, Logan is soaking wet. When they see the baby, about a second later, Logan is dry.
When the girl in the tower puts on her sarong, she ties it up at her right hip. After cutting to a brief shot outside and then back to her, the sarong is neatly tied up at her left hip.
When Logan comes over with Jason during Mitch and Hobie's dinner, the way he holds the baby changes between shots. In the close-up of him saying he'll tell Caroline, he doesn't appear to be holding a baby at all.
When Logan hands Jason to Mitch during dinner, the baby makes an audible cry even though he is shown about a second later with a pacifier in his mouth no one put there.
Logan makes Cody and Stephanie believe he has just come from a rescue by dumping a bucket of water over his head. However, they came in trucks with a clear view of the beach and the tower, so there is no way they could not have seen what he did.