I, for one, find Bernstein's apology to be sad and degrading. It is inconsistent with the virtue of pride. (Pride requires that we acknowledge and correct our moral failings, but not that we subject ourselves to a public humiliation of detailing those failings.)
For the sake of argument, let's presume that Bernstein did make a serious error in judgment in publishing his short comment in JARS. An adequate apology would be something along the lines of the following:
"I recently published a short comment in JARS regarding my CliffsNotes books. I was ignorant of the sort of articles and authors JARS publishes, many/most/all of which I emphatically do not sanction. I ought to have investigated further before giving my consent to publish. I do not approve of JARS in any way and will not publish in that forum again. I apologize for any confusion this incident might have created."
Such an apology would have conveyed the appropriate information and regret without going into the pathetic and demeaning details of whether Bernstein used or did not use his mind properly. (Those details might be relevant to a more personal discussion with a friend, but not to the whole world.)
An excessive apology can be just as damaging to trust and reputation as an inadequate one, I suspect.