She said publication of the particulars would not harm public safety and noted it was important the public have confidence in the New Zealand prison system.
"Where there have been inadequacies or deficiencies in the management of prisoners it is desirable that the public should have access to the knowledge of such deficiencies, that the deficiencies have been inquired into, and that steps have or will be taken with a view to ensuring that they do not occur again.''
Prison staff found Mills hanging and unresponsive.
A sheet tied around his neck was attached to the bars of a window, and a chair was found on the bunk near the window sill.
Ms Greig said 10 other prisoners had died in similar circumstances at Mt Eden Prison in a 15 year period starting October 1996.
In six previous findings between 1998 and 2005, coroners recommended Corrections modify the window bars in the prison cells.
Its failure to do so over cost considerations was a "serious omission", Ms Greig said.
"It is extremely concerning to this court that over a period of almost fifteen years the Department of Corrections did not address the clearly identified and recognised risk of the window bars in cells.
"The risks had been highlighted explicitly."
The Department of Corrections submitted that it had not ignored the previous recommendations, but had not implemented them because they would have required the installation of an air conditioning system in a prison that was due to be closed.
The closure of Mt Eden Men's Prison, built in the 1870s, was announced the year before Mills' death.
The department also submitted it was focused on up-front risk assessments, which it said were better than simply reducing hanging points - which could not be eliminated entirely, even in specialised cells.
Coroner Greig noted a letter found in Mills' cell made it clear he could no longer bear being in custody after six months and he would rather be dead.
The letter said he was disappointed he was not granted bail, found it difficult being labelled by the media and did not want to go through a trial.
It also raised concerns that he regularly did not get antidepressant medication he required.
At the inquest, Mills' lawyer Kevin Brosnahan said Mills had found being held custody particularly hard, which was compounded by other prisoners' awareness of his medical condition and the charges he was facing.
Mills had told his lawyer that prison was a lonely, frightening experience that he described as "the worst nightmare''.
His mental health had been assessed 12 times over the six-month period he was in custody, and each time he was found not to pose a risk to himself.
Coroner Greig found the assessments were properly done, but no specific consideration was given to the effect of moving Mills to different places of custody - particularly when he returned to the cells after a period in the infirmary for HIV-related health complications, and when he was moved from Auckland Central Remand Prison to the adjoining Mt Eden Men's Prison.
She noted Mills found the moves difficult and, while she was unable to make a finding on their contribution to his death, the moves had warranted closer monitoring.
Coroner Greig also found the administration of antidepressant medicine was not up to an appropriate standard, which "preyed on his mind''. The repeated failings to administer medicine were not acceptable, she found.
