What are some reasons for mathscinet listing a article, but then stating that there will be ``no review of this item''? In particular does it at all imply that the paper has little or no merit from a mathematical viewpoint?

$\begingroup$ The way to answer this is for someone to write to Math Reviews and ask them, no? $\endgroup$– Mariano SuárezÁlvarezOct 24, 2011 at 19:30

1$\begingroup$ Whatever the reason for not giving a review, my impression is that it is more common now than in the past. I might be wrong and I don't have statistics. If true, it is a negative development that reduces the usefulness of MR. $\endgroup$– Brendan McKayOct 25, 2011 at 0:48
3 Answers
You can see the "official line" here: http://www.ams.org/publications/mathreviews/mredit In particular,
Elementary articles or books, or articles that have not been refereed are ordinarily not listed.
In my experience, (and in addition to Thierry's and Andreas's list) this includes:
 Books reviews
 More problematic is the case of certain authors and journals who are, shall we say, excessively "prolific" sometimes one sees papers which are clearly "new mathematics" (or least, claim to be) but which do not get a review. For obvious reasons I won't give an example, but it's not hard to find using the MathSciNet search tool.
You ask "In particular does it at all imply that the paper has little or no merit from a mathematical viewpoint?". Well, certainly not, in some sense. A book review, or an elementary survey article, might well contain interesting mathematics, and might well be useful to read (which also one can clearly understand why they wouldn't get a review a "review of a review" would be quite silly).
As to my case (2.) above yes, perhaps this is Math Reviews (or an editor, or someone who was sent the paper to review) making that judgement. This does seem to be a grey area, as it's not covered by the "Editorial Statement" I linked to (except maybe in the word "elementary"). It would be interesting to get more information about this...

$\begingroup$ Book reviews! I knew I'd left something out! $\endgroup$ Oct 24, 2011 at 16:45

1$\begingroup$ Just to amplify the point 'or someone who was sent the paper to review': to suggest that there should be no review, is an explictly mentioned option for a reviewer. Compare ams.org/mresubs/guidereviewers.html under What is a review, point 2. $\endgroup$– user9072Oct 24, 2011 at 17:13
Sometimes publications (especially in proceedings volumes) are preliminary versions of papers whose final version will appear elsewhere. In such cases (or cases suspected to be such), Mathematical Reviews will wait for the final version. This is why papers in proceedings volumes that are final versions will often have a footnote saying something like "This paper is in final form and no version of it will appear elsewhere." This amounts to "Hey, Math Reviews! Review this."
There are many things that the Mathematical Reviews does not review. Off the top of my head,
 Nonmathematical items that may appear in mathematical publications;
 Many proceedings are not refereed, or if they are, the individual articles are not always refereed.
As to why MathSciNet would maintain a list of these items without reviewing them, I'm assuming that it's for the sake of completeness.