The Wrong Answer From a Little Bit of Right

Example 1:

"I checked my odometer; it's a shorter distance to go over that big hill than around it. Going over will save gas. Don't worry about the gas us use getting to the top of the hill; you'll get all that energy back when you start going down again."

No. Unless you intend on not using your brakes all the way down the hill, the vast majority of that hill-climbing energy is converted to heat (IE wasted) as the brake pads rub against the wheels. You're right only if you're okay with driving 90 mph when you get to the bottom.

Example 2:

"Fizz keepers don't work. Solubility of CO2 is only influenced by the partial pressure of CO2 in the container. Since air has negligible amounts of CO2, pumping air into the container won't do anything at all."

No. It turns out adding pressure from an inert gas slows the speed at which CO2 leaves the soda by lowering diffusion in the gas phase. Fizz keepers work, just not indefinitely.

Example 3:

"Because of the second law of thermodynamics, larger temperature differences between fridge's interior and exterior translate to greater efficiency. Therefore, your refrigerator uses less energy when it's hot outside."

No. The rate of heat transfer across the refrigerator's walls is proportional to the temperature difference between the fridge's interior and exterior. While your refrigerator might use less energy to cool down the air inside, it has to do so more often, so more energy gets used.

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You'll notice a theme here: each statement starts off by outlining a bit of knowledge, but still gets the wrong answer. I can only tear into these lines of logic because hindsight is 20/20. I, at one point, thought all of these were correct. 

What kills me is how much sense such statements seem to make until you know better. The real world is complicated. The only way to get good at explaining it accurately it is to make mistakes, but also recognize and correct prior mistakes as more knowledge is acquired. A little knowledge goes a long way... but if it stays little it's likely to cause damage or waste you money.