Respected journal uses only a single reviewer and has a high acceptance rate (>85%); could this be an acceptable practice?
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".