When the family gets stranded on the island, they do not bring any kind of luggage with them. By the time they sit by the fire, they've somehow acquired different clothes.
When Jesse talks to Rebecca above the waterfall, he raises his hand and extends two fingers and a thumb. In the next shot all fingers are extended, and in the next its only the two and the thumb again.
When Rebekah and Jesse are arguing on the cliff Rebekah has a colorful bathing suit cover up with long sleeves. When she jumps the cover-up is not visible. Likewise when she emerges from the water the cover up is gone completely.
DJ claims to have fished a clipboard out of the water, yet only the bottom left corner of the paper is wet.
When Joey is trying to hug his "dream girl", a red house is clearly visible, on a supposedly deserted island.
Ar around 13 mins, in the upper left corner, you can visibly see a red house. During this part of the episode, the Tanner family is supposed to be on an uninhabited island.
The boat the family rented should have an anchor that would've been more secure for the boat from drifting away.