Neither the council nor Ms Harrhy has commented on the reasons for her resignation, but it is understood that she realised too late that she was expected merely to act as a figurehead, with all the decisions being taken by the old boys club which actually runs things.
Anyone considering applying for the well-paid post when it is readvertised would do well to bear that in mind, but if you are willing to accept a big salary in return for asking "how high?" when told to jump, this could be the job for you.
The second point to note is the course of events which led up to Ms Harrhy's appointment. Back at the end of 2013 the council went through the lengthy and expensive process of trying to find a successor to Richard Workman, who was Director of Technical Services (now rebranded Director of Environment).
The cross-party appointments committee met to consider two candidates and was a whisker away from appointing one of them when, it is alleged, the chief executive decided that the councillors were about to make the wrong choice, and Cllr Meryl Gravell obliged by derailing the process.
The result was that the meeting failed to appoint anybody and Richard Workman was asked to postpone his departure, with the appointment of a successor put back for another year.
Peter Hughes Griffiths, who was then leading the Plaid group, was furious and made his feelings known in a meeting of the full council. In all his years as a councillor, this was one of the most disgraceful scenes he had ever witnessed, he said, and he pointed out the enormous waste of money involved.
In response, Mr James smiled sweetly and blamed the fiasco on political disagreements between the councillors.
A year and a half further on, and the council is gearing up for a third attempt to find someone who ticks the right boxes, with costs continuing to mount.
Perhaps Mr James should take advice from the College of Cardinals which regularly manages to select God's Representative on Earth with much less fuss and in much less time than it takes our council to appoint a senior director.
Mystery also surrounds the post of Head of Administration and Law where Mrs Linda Rees Jones clocked up what must have been a Wales all-comers record as "acting" head since the retirement of Lyn Thomas in 2011. By installing Mrs Rees Jones as acting head, Mr James avoided the messy business of having to get the appointment approved by councillors, and so matters remained until recently when Linda Legal suddenly began signing herself off as Head of Administration and Law, no longer just acting.
It will be recalled that the eminent lawyer and co-opted member of the council's Audit Committee, Sir David Lewis, described the quality of legal advice put out by Mrs Rees Jones's department as "cavalier at best and incompetent at worst".
Strangely this transformation appears to have happened without the involvement of an appointments committee.
Perhaps there is a legal loophole somewhere, or perhaps Mrs Rees Jones was canonised by the Almighty himself without the involvement of mere mortal councillors.