The "Ice from Fire" technique for using heat, ammonia and hydrogen was actually invented in 1824 by the English scientist Michael Faraday.
When Allie and his kids deliver ice to the primitive tribe, he unwraps the ice chunk and it had completely melted. He would have felt the weight change in his backpack.
At the end of the movie, as the family is going down the river to the ocean, a far shot of their houseboat shows a propeller wake, as if their outboard motor was running. They are drifting downriver.
During the hurricane, while Allie Fox and his family are being lashed by violent winds and nearly horizontal rain, a few palm trees in the background don't move.