I think that more than half of the articles and notes published in the Monthly contain original research. ("Totally original" does not seem like a useful standard, as many well-written seminal papers contain substantial portions which are not original research. I am currently translating Serre's 1972 paper on torsion points and am struck by the extent to which he was willing to be expository.)
I work at a large research university, I have two Monthly publications (and article and a note; the former appears in the December 2014 issue) and I happily -- indeed proudly -- list them alongside my other publications. There is definitely original research in both of these publications. (I apologize for the excessive horn-tooting, but it seems perhaps relevant to mention that Google Scholar finds a citation for each of these publications in a research paper written by people I have never met.) It is not the same species of research that I would publish in the Journal of Number Theory or Crelle, but since they occur alongside publications in these journals, I think their existence reflects positively on my research profile.
If you clicked on my webpage, you may have seen that I do separately list expository documents. These documents do not contain new results (though in some cases they contain proofs that I at least have not found in the literature). But I think it is not a coincidence that none of these documents have been published, although three out of the four have been submitted. I don't seem to have a good handle on the genre of "truly expository journal aritcles"; in fact, I find that it is as much work or more to get these published and I do think that the value to me would be smaller. There are also surprisingly few avenues for the publication of mathematical exposition, so because I am less interested in the certification or credit that the formal publication process brings, I have for a while been content to "self-publish" these results on my own webpage and/or the arxiv.
One default way is to list as research publications those which are archived and reviewed by MathSciNet. Alas I am not entirely clear on how these choices are made. It seems that in recent years, most Monthly publications get archived and many get reviewed. For the other MAA journals -- Math Magazine and the College Math Journal -- it seems to be rarer to have reviews. For instance my recent Monthly publication references a 2012 note of Kantrowitz and Schramm, but MathSciNet has no record of this publication. I just looked back at the last few years of CMJ, and I am a bit confused: I don't know why they don't list certain short articles (I think they should...) and how they choose to review the articles that they do.
Upon further thought, here are two rules of thumb I like a little better:
"Rule 1: Do not mislead". If your Nature publication is actually a letter to the editor correcting someone's birth and death dates [this is a totally hypothetical example; I have no idea whether this journal would ever publish such a letter] and you don't list this explanatory detail on your CV, I worry that you are trying to misrepresent yourself.
"Rule 2: Subject to Rule 1, make the publication list an accurate reflection of your own views." Thus, notwithstanding what I wrote above, I might perhaps submit this tiny note for publication in something like the CMJ someday. Unlike most other stuff I've written, it is wholly and sincerely aimed at actual intermediate-level undergraduate math majors, and I think that it might actually help some people if it were published. But there is just no mathematical novelty here, and I think it would dilute my own record by listing it as a research publication.