Expiration dates are a suggestion that's mostly about the quality of the product, ie, taste. It's not the same as "this product will turn into poison after X date".
All food is not created equal. Cheese can be aged for years, but once it enters the food-chain, it has to have an expiration date, which -in the case of aged, hard-block cheese - is essentially arbitrary, in the sense that mold that accumulates on the outside can be safely cut off, and doesn't impact the overall food quality of the piece of cheese you've bought.
What goes into your fridge can vary wildly in terms of actual expiration. Eggs, if stored properly, can hold for months.
If you have eggs that are past their expiration date, you can put them in a bowl of water to test their quality. High-quality eggs will stay on the bottom of your container. Less-fresh eggs will float in the middle. Eggs of "worse" quality will float on the surface.
That an egg floats on the surface is not the same as the egg being bad though. It just signifies that you should check it by cracking it open, and smell it. Chances are that they will be fine, but it's always useful to - ultimately - let your nose be your guide.
Potatoes and most root-vegetables will be fine for a very long time (months) if you keep them cool, dry and in a container that can breathe.
Most vegetables shouldn't be stored in a plastic bag, because it creates a micro-climate of excessive moisture and temperature that makes your produce age prematurely (and easily leads to mold, which, unlike cheese, you should be very careful about just cutting off, given the complexity of a lot of produce).
One tip, when buying groceries, is to go to the bread-section, because a lot of stores (at least in Europe) has free paper bags meant for bread. Paper-bags are superior to plastic bags when storing vegetables (of any kind), and a lot of these bread-bags are also perforated with small air-holes to keep the bread fresh.
These bags are significantly weaker than their plastic counterparts though, so use 2 paper-bags for the amount you usually put in a clear plastic bag.
Vegetables are generally much more lenient in terms of exceeding their expiration date, and many vegetables - mostly root-vegetables like potatoes, and garlic/onions, which seem to be inherently hostile to bacteria, and might be the easiest piece of produce to salvage simply by cutting out dark areas on its body.
Expiration dates are only really a concern with animal products, and especially if it hasn't been treated/processed in some way. Pickled fish could probably hold for months, if not years, but fresh fish, shrimp, and other sea-creatures can make you seriously ill if eaten beyond their expiration date, and could lead to death if given to people with weakened immune-systems.
Potatoes have been a staple-food throughout history for a variety of reasons. It's easy to cultivate, it's filling, and it can be stored for long periods of time without refrigeration.
If pirates could enjoy their 8-month-old potatoes on their raids, so can you, with your (I have to assume) barely 2 month old tatters.
If you frequently buy potatoes, be on the lookout for a small canvas sack. It's breathable, can alleviate excessive moisture-accumulation, and is durable enough to be used for years, in a way that your average paper-bag probably can't.
That said, if any of the potatoes you just ate had a green tint to its skin, there is cause for concern. Green-tinted potato skin contains a substance that is harmless to most animals, but when eaten by humans, is metabolized as a poison, similar to mercury, in the way it can seriously damage your nervous-system in high doses.
Small doses of this substance is not a big deal - even if it's obviously not optimal to ingest any kind of poison - but if two or more of the potatoes you just ate had green-tinted skin you should definitely not shrug it off, and keep it in mind if you suddenly experience adverse health-effects.
