Revealing mistake: The "sand" on the beach of the supposedly lonely island Blanche, Rose, Dorothy and the three men stranded on is one solid cloth made of a rubber-like material. It wobbles and bends whenever a character's feet are on-screen.
Plot hole: It shouldn't matter if the neighborhood's got a petition. If the tree in question is on Mrs. Claxton's property then they wouldn't have a say in the city removing it.
Answer: Ice makers were a new invention, advertisement purposes.