Post apocalypse. What resources will be most abundant or useful if mined from Twentieth Century landfills. Easy things like steel and aluminium are obvious, but what else is likely to be worth digging up? And after one hundred years would buried organics in landfill still be producing methane in concentrations worth tapping?
In most post apocalypse scenarios, the manufacturing base is gone, and so is refrigeration. Reusable, sealable containers+lids will go a long way to preserve what foods there are. Canning jars and lids would be true prizes -- and could become trade items in/of themselves.
Note also that clear PET bottles (most clear soda bottles) pass enough UV light that one can sterilize water by leaving it out for long enough in full sunlight. See: https://en.wikipedia.org/wiki/Solar_water_disinfection#Process_for_household_application
Concerning shopping, my mother-in-law had a simple and practical phrase:
If you don't need it, it isn't a bargain.
Curiously, this applies to our situation. If our recovering peoples don't need it, it's not valuable for them to obtain it.
Methane cometh from pig...
Mad Max Beyond Thunderdome kindof sensationalized the idea that if you get enough pigs together in an enclosed space you can electrify a small town.
You see, the left side of the equation is relatively simple. Boil a lot of water and use the steam to turn a crankshaft. It's the right side of the equation that's the real bounder. Electrical generators, transformers, switches, motors, blah, blah, blah. And where do you get new light bulbs, Max, anyway? Huh?
Basically, if you have the technology to electrify the town there are probably easier ways to generate the power than drilling in landfills for methane. However, if the technological balance works (frankly, it won't, but if it does...) then deep landfills in warm, damp areas (think southern costal) will generate methane almost forever.
But if people are basically back to hunter-gather with houses (i.e., up to the 1500's or like pioneers, seperated from society), then they'll never go to the effort to sink a well for methane, they'll just burn cow dung and wood unless all that other stuff is a very limited resource.
People are very practical. If there's an easier way to do it, most people will do it that way. You need to force people to do things the hard way.
I want to say just one word to you—just one word... Plastics!
The real issue is what is practical to mine. With no research and no better knowledge than what I can find scratching my left ear, my guess is that the single biggest resource in any landfill is plastic.
Plastic is indispensible to us today, but to a pioneer-style community? It's primary value would likely be sheeting for structures and basic implements like eating/cooking utensiles. Maybe arrows (at least shafts). Almost anything you can do with wood you can do with plastic — assuming it's not simpler to get the wood.
Practicality will be a big factor here. Plastic is easy to burn and once it burns, it's useless. If your post-apocalyptic pioneers have easy access to anything that substitutes for mining the landfill, they'll avoid the landfill.
So, other than the obvious metals, what else is there?
Old sofas and worn out electronics have little value. But, according to here, there is only one other useful thing:
Oh, yeah. You want glass. It's as valuable as metal. The earlier the "technology" of your pioneers, the more valuable glass becomes. It's easy to shape and doesn't rust, making it a good long-term container for any fluid. It's easy to sharpen and easy to replace. It can keep things out and keep them in, like light and heat. Shape it the right way, and you can make a fire or advance science.
Frankly, glass is probably the most important thing you can mine from a landfill.
Note: Surprisingly (and discovered after I wrote the section on plastic), the largest single item type in a landfill by far is paper... but paper has little value to pioneer-stage and earlier peoples other than as toilet paper. And that assumes it hasn't decayed to the point of being a statistic in principle more than a statistic in fact.
@ Landfill methane gas
yes if the landfill was big enough, compact enough, and not overly tapped could potentially still produce methane for over 100 years.
A post apocalyptic society still in reconstruction would be more concerned with basic life necessities like providing power, water, and waste management. All of those could be met with resources still obtainable on the surface and metals you mentioned. One possible desireable is fertilizers. An organic landfill would be a good source for fertilizers though potentially a health concern at the same time.
An enduring society however, desperate for raw resources to feed its consumerist market would inevitably turn to recycling or generalization in order to keep up with demand. By generalization I mean achieving the same capabilites only with cheaper (more common) materials.