Residents' spokesman Mike Brennan, 69, said gutters and drains were blocked by leaves but he believed the tiled roof and its guttering were never up to handling heavy rain.
He was concerned about health and welfare in a complex where ages range from 65 to 95.
In one unit, he showed the Herald mould on walls and the rotting wooden sill of a south-facing bedroom window.
Mr Brennan said this was the result of seven years of leaks.
The resident of another unit had not slept in the bedroom for two years because it felt damp.
Patches of black mould coated much of the high-pitched ceiling and east-facing wall, spreading to the spare room and out-of-reach places in the main living areas.
These conditions prevailed in spite of units being inspected by the landlord three times a year, said Mr Brennan, who has been a resident for nine years.
He said units were upgraded only when the occupants left, and he was seeking a Tenancy Tribunal direction to replace the roof and gutters. After the Herald visit and its inquiries, Housing New Zealand regional manager Neil Adams said the corporation would arrange for the ceilings to be cleaned for tenants.
He said the corporation spent $120,000 on maintaining the properties. He expected repair work on the roofs would start within a week or two.
Contractors would work progressively through each block of units and then work would start on upgrading the interior of all 25 units. The result would be $200,000 spent to get "warmer and drier homes for all tenants", he said.
At the Ellerslie complex of 66 units, some residents, who asked not to be named, said complaints about mould inside units prompted notice of a "health and safety" inspection.
Corporation general manager Kay Read said the leaking started after heavy rain in May and June.
"Because tenant welfare is our highest priority, we immediately relocated five residents living in units next to the leaking block wall to alternative accommodation while we make repairs to the wall and their units," she said.
"We are testing 12 other units which are also next to the block wall."