Let me give some examples from my own writing, mostly just to fix ideas. (I am do not trying mean to complain.)
This is not a sad story for me overall because I learned more about the problem ("The Diophantine Problem of Frobenius") in writing the second version with Gil. But still, something is lost: the first version was a fairly faithful writeup of a talk that I have given to advanced undergraduate / basic graduate audiences at several places. For a long time, this was my "general audience" talk, and it worked at getting people involved and interested: people always came up to me afterward with further questions and suggested improvements, much more so than any arithmetic geometry talk I have ever given. The main result in our JIS paper is unfortunately a little technical [not deep, not sophisticated; just technical: lots of gcd's and inverses modulo various things] to state, and although I have recommended to several students to read this paper, so far nothing has come of it.
2) A couple few years ago I managed to reprove a theorem of Luther Claborn (every abelian group is isomorphic to the class group of some Dedekind domain) by using elliptic curves along the lines of a suggestion by Michael Rosen (who reproved the result in the countable case). I asked around and was advised to submit the paper to L'Enseignement Mathematique. In my writeup, I made the conscious decision to write the paper in an expository way: that is, I included a lot of background material and explained connections between the various results, even things which were not directly related to the theorem in question. The paper was accepted; but the referee made it clear that s/he would have preferred a more streamlined, research oriented approach. Thus EM, despite its name ("Mathematical Education"), seems to be primarily a research journal (which likes papers taking new looks at old or easily stated problems: it's certainly a good journal and I'm proud to be published in it), and I was able to smuggle in some exposition under the cover of a new research result.
[Added: And a newer version: http://math.uga.edu/~pete/factorization2010.pdf.]
Added: Looking back at the In my factorization paperjust now (the first time in some months), I found something which I think is relevant to the issue at hand: I compare (unfavorably!) my paper to build on similar expositions by the leading algebraists P. Samuel and P.M. Cohn. I think these two papers, published in 1968 and 1973, are both excellent examples of the sort of "intermediate exposition" I have in mind (closer to the high end of the range, but still intermediate: one of the main results Samuel discusses, Nagata's Theorem, was published in 1957 so was not exactly hot off the presses when Samuel wrote his article). Both articles were published by the American Mathematical Monthly! I don't think the Monthly would publish either of them nowadays.
Added: I have recently submitted a paper to the Monthly:
(By another coincidence, this paper is a mildly souped up answer to MO question #26. But I did the "research" on this paper in the lonely pre-MO days of 2008.)
As far as comments on the paper are concerned
(Added: they are most welcome, but I ask that you send them to me privately unless you feel that they have some bearing on it was accepted by the general discussion at hand. Monthly.)