The display area in the Link Gallery was not sprinkler-protected, while there was poor coverage in the Māori Gallery.
There was not sufficient clearance between the main 100mm water pipe and the concrete walls it passes through between the museum/gallery building and the Century Theatre building.
"It would appear that any significant movement will shear the 100mm main at this point," the report said.
Napier City Council said in response to questions made under LGOIMA that it was withholding the names of the companies involved in the 2013 renovation of the building.
It said it was prioritising the completion of remedial work before looking into whether legal action is appropriate.
"Further investigation into this matter is required before Council will be in a position to make a decision on legal action or otherwise."
The Century Theatre reopened on January 27, and NCC anticipates public areas of the library will be open by the end of March or in early April, with work on the rooms occupied by museum exhibits likely to take longer.
Council said it could not confirm how much all the remedial work would cost until all the defects were addressed.
"It is anticipated that the works will be completed before the end of June 2021 and Council will then be in a position to confirm costs."