The so-called '49 Pontiac' does not appear to be entirely a 1949 as described. If you look at the car carefully, you will notice it has a 1950 grille, the hood and trunk - 1951. The side molding trim on the front fender - seeming like half a feather or arrow is 1951, the stone-shield on the back fenders either 1949 or 1950 ('51s and '52s triangular) - it was that for both years. Pontiac had that basic model from 1949 through 1952, with varying grille, trim differences.
Andy fires paper cups out his right hand bedroom window towards the moon. He then moves to the left hand window and climbs out on to the roof. The moon is now in a different part of the sky and he could not have seen it from the other window.
The reunited family take the amphibious car across a lake to Canada from the Spires of the Moon National Park. When Washington showed Andy the map however, the Spires of the Moon was ringed in red on the map and it was hundreds of miles from the Canadian border.
At the gas station, the attendant seems to open the hood (which is actually the trunk) by popping something like on a normal car. The trunk and hood on an Amphicar are opened using a large key about 10" long that must be inserted and turned individually - two locks in front and one in the back.
As mentioned in the film, it took 19 hours for the Apollo astronauts to land on the moon from the moment they lifted off, and has Washington and Andrew traveling over that same span of time. However, by counting the number of nights they have on the trip, they are on the road for three days.