If you boil water inside a pot the outer rim bubbles first, I imagine because its hotter. Does that same concept apply for the inside of a refrigerator for example. Is the outer rim always more extreme, or at least at first?
When you are boiling water bubbles typically form first at the bottom of the pot, and then at the walls. As you guessed, this is because the bottom is usually at higher temperature than the walls, since it's in direct contact with the heat source. The reason that bubbles don't appear sooner in the bulk of the water is that nucleation (the initial formation of tiny bubbles) is easier at surfaces and at their irregularities. To check this, you can use any pot with a big scratch, and you'll see bubbles forming at the scratch first.
In a refrigerator, the conditions are quite different. In a typical refrigerator there's a coiled set of pipes inside the freezer, near the top of the unit. This is the evaporator, and it's where the heat is extracted, and this is where you'll have the lowest temperatures. If the leaks are small, you'll have the lowest temperature at the top and the highest temperature at the bottom. Usually, the back of the refrigerator is colder than the front because heat leaks mainly through the door crack.