"How do we encourage edits to obsolete/out of date answers?"
[Disclaimer: Actually read all the Answers and most of the comments - whew]
The problem has likely come about from a combination of The Rules, human nature, the way the site is setup (page layout), rewards (psychological, numerical, perceptual, expediency), etc. - this is evident in many of the answers.
Clicking on "Questions" takes one to the main Feed where the (under) Banner goes: "All Questions ... Newest - Featured - etc.", but there's not an "Oldest" where people could go to be nostalgic, to find questions known to have newer answers, or to hunt for things to suggest for deletion.
We promote 'new questions' as better (or more interesting) by not only having a link to click for them but likely the belief that answering the new questions correctly and quickly:
Rewards the answerer with UpVotes (with nothing to compare to),
Provides the possibility of being The Chosen One (usually viewed as good, sometimes an insult - to suggest that you are special),
Self-promotes one as the sharpest knife in the drawer.
In the interests of keeping this answer as short as possible while still being useful I propose:
A 'Legacy Review' Queue - While waiting for new questions or for one's question to be answered people could be encouraged to poke around where they could suggest an improvement and score a point. (Add "Oldest" to the end of the sub-banner Menu where "Newest" appears).
Maintenance Points - Approved edits, deletions, improvement, etc. score a point.
Trivial Edits - After accumulating enough reputation allow trivial edits (currently the minimum limit is a few characters must be changed). A good example is updating the question "How many Planets in our Solar System" or "How many Moons does Saturn have" - those answers don't require a big edit but they do need a current answer. It's also nice if someone reputable can fix a single annoying spelling mistake in an otherwise good question or answer.
The 'presentation order' for the answers should be:
Chosen answer first (as someone who's question is accepted is the one who accepts the answer). The Mods can still delete unwanted chosen answers, bumping it back down to unanswered.
Highest voted answer next.
Highest trending answer third - new correct answers should rise up over legacy unchosen and lessor-popular answers.
For some sub-sites a versioning system is appropriate, so we have the newest version's first three followed by the next version's first three, etc. followed by the rest, and the newest (low votes) untrended answers at the bottom.
Whatever is ultimately decided upon should be relatively simple, intuitive, cross-site implementable (with a provision for sub-sites to exempt themselves when applicable).
We can encourage edits to obsolete answers by providing a means to funnel people towards helping with them, to donate a half-hour during their visit, and score a few points, maybe a "Hundred hour Maintenance" Badge - it's not much but that's all we got.
I'll leave it there in the interests of not adding yet another lengthy answer to be read when there exists so many already and avoid contributing to the problem this question wishes to solve.
