One trick that my advisor, Ronnie Lee, advocated was to use a descriptive term before using the symbolic name for the object. Thus write, "the function $f$, the element $x$, the group $G$, or the subgroup $H$. Most importantly, don't expect that your reader has internalized the notation that you are using. If you introduced a symbol $\Theta_{i,j,k}(x,y,z)$ on page 2 and you don't use it again until page 5, then remind them that the subscripts of the cocycle $\Theta$ indicate one thing while the arguments $x,y,z$ indicate another.
Another trick that is suggested by literature --- and can be deadly in technical writing --- is to try and find synonyms for the objects in question. A group might be a group for a while, or later it may be giving an action. In the latter case, the set of symmetries $G$ that act on the space $X$ is given by $\ldots$. Context is important.
Vary cadence. Long sentences that contain many ideas should have shorter declarative sentences interspersed. Read your papers out loud. Do they sound repetitive?
My last piece of advice is one I have been wanting to say for a long time. Don't write your results up. Write your results down. You figure out what I mean by that.
According to the article, the original data was provided by the AMS. I don't think that the AMS leaves this sort of data lying around on laptops on trains, so do to it again you'd have to go and ask them. I suspect that, quite reasonably, the AMS likes to know what uses their data is put to.
On the other hand, data can be mined very easily from the arXiv via the API. I don't know if arXiv data would suffice for you. If so, a little scripting showed the following data for the month of October:
math.CO: 36, 38, 11, 7, 2, 1
math.CA: 9, 11, 5, 1, 1
math.CT: 4, 4, 3
math.GN: 6, 7, 2
math.AT: 18, 9, 2
math.AC: 6, 9, 4, 2
math.CV: 24, 16, 1
math.OC: 6, 11, 5, 3
math.MG: 7, 7, 4, , 1
math.HO: 14
math.DG: 43, 48, 16, 3, 1
math.LO: 9, 2, 2
math.RA: 12, 11, 7, , , 2
math.ST: 3, 14, 2
math.PR: 43, 45, 25, 7
math.GT: 29, 22, 4, 2
math.SG: 13, 4, 2
math.GM: 8
math.SP: 7, , 4, 1
math.FA: 22, 18, 9, 4
math.OA: 9, 6, 4, 3, 1
math-ph: 52, 53, 15, 2, 1
math.DS: 23, 17, 9, 2, 1
math.QA: 13, 13, 3
math.KT: 3, 1
math.GR: 17, 27, 3, 2
math.NA: 4, 13, 9
math.RT: 28, 14, 3
math.NT: 48, 31, 8, , , 1
math.AP: 49, 59, 29, 4
math.AG: 69, 34, 11, 1, 2
Total: 634, 544, 202, 44, 10, 4
Average: 0.44, 0.37, 0.14, 0.03, 0, 0
The ordering is by number-of-authors. So for math.KT there were 4 papers, of which 3 were single authored and 1 with 2 authors. Missing entries are 0s (so in math.NT there was a 6-author paper but none with 4 or 5). So collaborations outweigh single-author papers by a little bit (technical term).
Best Answer
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...