**Update**

In view of Zero's excellent Answer, I should point out that my Answer ignores the question of **energy efficiency** and addresses only the issue of **temperature stability**. I agree with Zero that this practice is not likely to save energy. 

**Original Answer**

Much of the food you place in the freezer will have a high water content, so if you keep the freezer full of food there is no need for bottles of water. The food  provides the "thermo-inertia" which your Dad recommends, and minimises space for cold air which falls out and is replaced by warm moist air at room temperature when you open the freezer door. (Having a chest freezer avoids cold air falling out. So does keeping food in drawers.)  

[**Note** : Fridge manufacturers recommend not over-filling. Leaving space for cold air to circulate helps keep the temperature uniform.] 

But if you are not able to keep the freezer full, it is an excellent idea, for the reason your Dad gives. You should fill as much space as possible in this way, while trying to avoid having to remove frozen bottles of water, which will thaw and have to be re-frozen later.

Although filling the empty space with blocks of polystyrene (polystyrol) will save energy, avoid the warm air intake problem, and reduce conduction of heat **into** frozen food, it will also reduce conduction of heat **out of** food which is not yet frozen. This increases the time it takes for food to freeze, which increases deterioration because the food is at a higher temperature for longer. The polystyrene will provide almost no "thermo-inertia".

Other useful discussions :

[Seasoned Advice SE : Does keeping a freezer full significantly help energy efficiency](http://cooking.stackexchange.com/questions/57957/does-keeping-a-fridge-freezer-full-significantly-help-energy-efficiency)  
[Skeptics SE : Does keeping a fridge or freezer full improve its energy usage?](http://skeptics.stackexchange.com/questions/10527/does-keeping-a-fridge-or-freezer-full-improve-its-energy-usage)  
[Physics SE : Does an empty refrigerator require more power to stay cold than a full one?](http://physics.stackexchange.com/q/61445)  
[The Straight Dope : Does a refrigerator cool more efficiently when full?](http://www.straightdope.com/columns/read/2657/does-a-refrigerator-cool-more-efficiently-when-full)