I'm presenting this in numbered sections so that people can respond specifically to what they agree or disagree with (please leave a comment such as "Disagree with Proposal 2" or "Agree with Proposal 4"). I'm not going to defend or justify Assumption 1 now since I suspect it is not highly contentious and want to focus on an idea for a solution.
Assumption 1. EL&U currently has a lot of questions that deserve to be improved. The main content and meaning of these questions is appropriate for this site, but the questions are presented poorly and could possibly also benefit from added context or detail.
Conjecture 1. It would benefit the EL&U site and community if more of its members could edit posts that deserve to be edited. Such posts include posts whose core content has merit. Such edits include fixing disruptive spelling and grammar mistakes; adding links and references; and adding context, supporting evidence, or details to make a question more complete.
Conjecture 2. Lowering the reputation required for all users to edit posts could have lots of bad consequences, such as lots of bad edits happening.
Conjecture 3. EL&U already does and should have a team of editors because SE sites are a mixture of Q&A and wiki.
Proposal 1. The leaders of EL&U should be able to selectively allow some EL&U members who are not automatically members of its editing team due to insufficient reputation to make edits. These members should be selected based on a demonstration that they understand what makes a post on EL&U bad, good, and great.
For example, I have been on EL&U for only a few days and only have ~450 rep (101 of that from the SE network). I would gladly edit questions here to make them better because I enjoy it and think it is very useful. But I don't have many questions to ask on this site, and since I generally spend a lot of time on my answers, I don't have time to answer lots of questions. Once classes start next week, I won't have much time to answer questions at all. So I am unlikely to earn enough reputation to be able to edit questions here. (I know I can suggest edits and will be doing this more often now. See Proposal 0 below.)
Proposal 1.5 In order to focus the manually-promoted editors and avoid problems, there should be a restriction on their editing privileges, such as to editing questions only or editing posts by people whose reputation is under a certain high amount.
Proposal 0. The ability of users to suggest edits is already sufficient for handling the editing needs of EL&U.
Proposal 2. EL&U should add a type of flagging mechanism so that every post that deserves improvement by editing can be flagged so that the editing team can find them easily, e.g., by flagged posts appearing in a list somewhere.
Proposal 3. The proposed flagging mechanism should not affect the vote of the post or reputation of the poster in anyway.
Proposal 4. The proposed flagging mechanism should increase the reputation of the flagging user by some amount, provided that the post is not already flagged. Suggested amount: +1.
Proposal 5. The proposed flagging mechanism should not increase the current workload of the moderators.
Proposal 6. The editing team and ability to edit posts should be highlighted occasionally to make users aware of its existence and benefit.
Proposal 7. Make the edit button on a post more prominent, possibly with a tooltip saying that editing to improve posts is encouraged. [Broken out into a separate question. Please vote there.]
Summary. I have three main, unrelated suggestions: (A) selectively let more people edit, (B) add a feature to flag posts that deserve editing so they can be more easily found and improved by others, and (C) encourage people to edit things that deserve editing; the only sign that I see that questions even can be edited is the small, low-contrast, text link at the bottom of the question.
[Note: the two threads (1, 2) that I found related to relaxing the editing requirements were generally in favor of it.]
