Water reaches maximum density at +4C, that is why ponds freeze from the top downwards.
About the floating ice...yes it does effect water levels. Fill a glass COMPLETLEY full and put three ice cubes in it....duh.
The point with that experiment is that you have a full glass but are adding water to it, frozen or not is immaterial, if you add liquid water, it will still overflow.
A better experiment would be to take a full glass of water and freeze it. Since water at 0C is less dense then water at 4C, it will expand, and either rise above the rim of the glass or break the glass, (depends on the geometry and smoothness of the glass). In the interval between +4 and zero, the expansion will be enough to make some of the water overflow the glass.
Actually - for a complete truth, it depends on the definition of "full". If the water level in the glass is exactly level with the top of the glass, surface tension will allow the level of the water to rise above the top of the glass without spilling, simple analogies like this suffer from these kinds of failings.
As to the film, never let the facts stand in the way of a decent special effects budget.