Respected journal uses only a single reviewer and has a high acceptance rate (>85%); could this be an acceptable practice? I have recently noticed a failed case of peer review at The Astrophysical Journal (ApJ). It is a solid journal in which researchers of astrophysics can present good science without worrying about the topic being fashionable (as opposed to, e.g., Nature and Science). The peer-reviewed paper in question was published in ApJ but retracted by the journal within a week after it was reported as a case of plagiarism.

However, the issue I'd like to raise is not about plagiarism but about the review process of the journal. In the aforementioned paper, there are obvious technical errors that do not even pass a basic sanity check. I believe that had it been properly reviewed, the paper could in no way have been accepted in the first place, plagiarized or not.

(For more information, see my comment on Jeffrey Beall's blog post about the incidence of plagiarism. Moreover, my Astronomy SE post contains some technical details. The latter was posed as a question but I'm now sure that my suspiscion---that there are blatant errors in the paper---is well-founded. I had at first shied away from the obvious conclusion just because I have no expertise in astrophysics.)

It is disturbing that the acceptance rate of the journal is very high (between 85--90%) while only a single referee participates in the review process. (ApJ seeks an additional opinion only if the acceptance decision cannot be made without one.) As the low quality of the retracted paper demonstrates, any such a single-reviewer model falls apart when a referee hastily signs off the paper.

This incident seems to show the poor review process of ApJ. Could this be justified simply on the grounds that no better practice is available in the field? Or is this worrysome even after acknowledging that academic customs greatly vary across different fields?
By saying 


  This incidence demonstrates the poor review process of ApJ


you are already asserting an answer to your question.  What you can say based on the facts you have presented is that the peer review process failed in one instance.  The document you have linked indicates that the ApJ publishes roughly 4,000 papers per year, so one failure per year would represent just twenty-five thousandths of a percent.  Extrapolating based on that seems wrong (and in any case, you haven't mentioned any failures of the system in previous years).

The term acceptable refers to agreement of a group of people.  The refereeing process of the ApJ is clearly not only "acceptable", but in fact accepted, as it is a leading journal in its field.

More generally, should a high acceptance rate be a cause for concern?  Independent of other indicators, I think the answer is no.  A high acceptance rate for a leading journal may be surprising to researchers from other fields.  But it seems the ApJ is mainly interested in the correctness of a paper (rather than, as you say, whether it is fashionable).  So the acceptance rate should depend on the ratio of correct and incorrect papers submitted.  Here of course "incorrect" means fundamentally incorrect and unfixable.  I don't know of any fundamental reason that there must be a large fraction of incorrect papers.

Should the use of a single referee be a cause for concern?  For many (including myself) this is very surprising and goes counter to familiar practices.  But the ApJ is being up-front about this, so any group that wants to change the practice could start a new journal or lobby the editors of the ApJ.  I think this question is one the astrophysics community should handle for itself.  So far, their answer seems to be "no".