Math Annotate Platform? Suppose most mathematical research papers were freely accessible online. 
Suppose a well-organized platform existed where responsible users could write comments on any paper (linking to its doi, Arxiv number, or other electronic identifier from which it could be retrieved freely), or even ``mark it up'' (pointing to similar arguments elsewhere, catch and correct mistakes, e.g.), and where you could see others' comments and mark-ups. 
Would this be, or evolve into, a useful tool for mathematical research? What features would be necessary, useful, or to-be-avoided-at-all-costs? 
This is not a rhetorical question: a committee of the National Research Council is looking into what could be built on top of a World Digital Math Library, to make it even more useful to the mathematical community than having all the materials available. This study is being funded by the Sloan Foundation. 
Input from the mathematical community would be very useful.
 A: I think that such a platform would be extremely useful, 
but it also would need strong moderation to remove misuse, perhaps only initially.
The moderation effort is not at all trivial as the experience of the arXiv moderators shows.
A: If this forum were a mathematical discussion forum, your question would be welcome, encouraged,
and anticipated.  I would be happy to provide input from a public citizen point of view.
This forum is meant more for answers, references, and perhaps derived questions.  While I hope
you get some appropriate input from here, I instead encourage setting up a wiki or participating
in a forum like publishing.mathforge.org, which has been discussing related issues for a while.
I believe (after gathering a few search terms from suggestions about to appear) that you will
find a lot of the discussion extant on various weblogs and related fora, and that you will see
a number of issues to be avoided at some cost.
As with most community efforts, you will find the greatest success coming from a dedicated subcommunity
which understands and represents the core values of the effort.  Assemble that, and much of the rest will follow.
It is my hope that what you propose will permit and benefit from contributions from the interested public.
Gerhard "Not A Professional Mathematician (Yet)" Paseman, 2013.02.17
A: I think such a thing would provide immense value.  In particular I can think of instances when the following sorts of comments would have saved me a great deal of time: 
(1) No need to read pages XX-XXX, here is a one paragraph argument.
(2) This result has since been strengthened, see ...
(3) The following claims are not quite right, here is a counterexample, and here is how to fix it.
(4) The following claims actually are right, even though the following might at first seem like a counterexample.
(5) What the author really means by [SGA] is [SGA N, page XXX]
(6) This result has the following interesting applications ...
(6a) What would be even better is an automated system where, not just can you see what papers cite a given paper as you can today, but you can even see where a given lemma or proposition is cited.
(7) The author has only cited the relevant papers of his friends, the following other work in the subject is closely related.
(8) This paper is actually much less / much more interesting than it sounds...
(9) The following seems to be a gap in the argument:
(10) This 200 page paper assumes along the way in places which are explicit but maybe you didn't notice the following conjectures...
I think it would be essential however to ensure that people post under their own names and other measures are taken to ensure responsibility and measure the credibility of authors, but I think at the present stage of development of the internet we know how to do that.
I also think items like (3), (4), (9), (10) will become increasingly important; already it seems that people who consider themselves sufficiently famous don't necessarily bother publishing in journals (and so are not subjected to the review system), or even if they do are perhaps sufficiently famous to override or intimidate the reviewers, perhaps by sheer number of pages, etc...
A: Having read and followed numerous discussion on the subject,
it seems that possible downsides arise from having comments or discussions unwanted by the authors of the article. 
However, enabling the authors to moderate all comments themselves would seem
to address those concerns. That is, when the authors would receive the comments first and then decide whether to make them public. Of course, that would include  the possible decision by the authors not to receive any comments at all, a decision that they should also be able to reverse at any time in the future.
Basically, since the authors are the ones who wrote the paper, they should own all the corresponding rights, including any comments and moderation. 
A: Git is a version control system which is commonly used by programmers.  While it is useful for managing ones own individual projects, it really starts to shine in collaborative situations.  While it was designed to help programmers, it is really a great system for anyone trying writing any text based project.  This includes math papers.  
The advantages are numerous:
The entire history of the document is stored, so that information is never lost by writing over a document.
The contribution history is clearly documented, so you can see who is responsible for different parts of the work.  This very nicely solves attribution issues.
The workflow for working together collaboratively is wonderful.  If you and another person are working on different parts of the same document, or making changes to different files altogether, git will merge your work without any effort on your part.  If there is a conflict between the work done, git alerts you to this, and allows you to resolve these conflicts.
It takes a little getting used to, but I now find it so essential to how I work that I use it for everything.  I wouldn't dream of writing a paper without using git to help me manage versions, especially if I am working on it with another person.
Github provides a free method for people to host their papers, and allow others to collaboratively edit them, comment on them, make "bug reports", and so on, which I feel would be of great value to the mathematical community.
I think that Git really does solve all of the problems raised by the OP.
A: Internet group according to "Art of Agreement"

Index


*

*Axioms

*Implementation: bees & hives

*Practical considerations

*Philosophy




Axioms


*

*Freedom of Speech (of posting)

*Freedom of not listening (of not seeing, of not reading)

*Responsibility (for posts)


*

*Axioms 1-2 imply that everybody and nobody is a moderator, i.e. every participant $X$ is a moderator for $X$, and for nobody else.

*Responsibility means that no post gets ever erased (it may be declared obsolete though, while it is still available to the public)--think of wiki's history.






Implementation: bees $\&$ hives
It's a highly decentralized system (tightly glued together by links, see below).
Some mathematicians may start hive Art of Thinking. Some other people may start hive Mathematics 2013++. There is no need for more than one hive devoted to mathematics but if that's what they want, nobody will stop them.
Hives form a partially ordered set. You may start a Geometry hive, and declare it to be under Art of Thinking, but above Euclidean Geometry hive. More about the organization of the world of Bees and Hives later.
You start a hive by yourself or with others by simply agreeing on its name, and by creating bee sites, which declare that they are, say, a bee site of Art of Thinking or of Mathematics 2013++, etc. Each participant, a bee, has their own Internet place under their own exclusive control. Typically, a bee (a participant) is just one person (Internaut).
The goal of a hive is to create a dynamically growing data base of posts (texts) and tables of contents, i.e. tables of links to other tables and to posts.
As a bee, you write mainly texts (research, comments about posts by other bees, teaching materials, etc.), but also tables which organize your bee site, which allow readers to navigate your bee site. Your tables may go beyond your own site, they may include links to any posts and tables within your hive. Of course you may also promote any materials, and you may have links to any Internet pages--but that would be more like writing an article (for your hive), for instance something like "Internet resources concerned with mathematics of XVIII century"--it would not be a part of hive's partially ordered hierarchical organization.
If you are socially inclined then you may declare yourself an administrator (with no power though), and then you  create a hive site, say for Art of Thinking, e.g. Internaut $X$ may create site titled: Hive Art of Thinking by $X$. The difference between a bee site and a hive site is the intent. In the case of a hive site you want to serve the whole hive rather than just your own bee site.
There can be several hive sites (administrative sites) for the same site, just any number of them. Administrators create table by including the links selectively (rather than all of them).
Any bee or administrator may maintain lists of scores which evaluate posts and bees. Finally, bees and administrators may provide tables of posts and bees which should be avoided.


Practical considerations
Realistically speaking, the described system has a chance only if some (relatively simple to code) software will be created, so that maintaining the tables of contents will be easy. For instance, you may like to copy someone else's several tables, and adopt them for your own bee site after some modifications. The software should also protect you from running into material which you declared to be avoided, e.g. when you want to avoid what administrator X suggests to avoid. Care always has to be taken to avoid loops, to follow always a partial order (rather than a tree--the tree organization is often not adequate).


Philosophy
Art of Agreement is based on one commandment only: you shall not impose.
This commandment applies to adults of sound mind. It's not something to discuss. You either accept it or not. You may only discuss whether or not Art of Agreement leads to better economy, to higher quality of life, etc.
The above bees & hives organization is an example. It should work not because an authority (like wikipedia teen editors) is moderating things for you, including the moderation of you. Instead, you yourself choose your authorities which you follow voluntarily (to whatever extent you choose), and whom you may drop at any time, whom you may replace with other authorities, etc. Why, you may be an authority yourself :-)
Good mathematicians easily recognize other good mathematicians. They would read each other, and they would read papers by unknown to them authors, who are recommended by good mathematicians. The recognition spreads around easily and quite fast. This way a high quality body of mathematics is created and collected without being adversely affected by more numerous weaker articles. And all this judgmental notions of "good" (partially subjective, partially objective) are custom taylored to each bee (which is nice, I feel :-)).
