My last apartment was about 11 years old, and it was obviously remodeled a little in one room (tatami room). I suspect it was because of mold behind the walls. Neighbors upstairs had similar problems, so it wasn't the fact that we were on the ground floor where cement foundations might lead to mold.
I think tenants don't say much because they may be out soon (2-year leases, and businessmen transfers, and all), or just because Japanese people "gaman suru" and tolerate things (shoganai) more than we do.
My apartment had serious mold growing up from the floorboards in one bedroom and the living room. Ten inches up! Despite running a dehumidifier almost constantly, the humidity was never below 60% and usually 80-95% year round. We cleaned the floorboards 3 times daily and still ended up with mold there and behind many pieces of furniture.
My wife refused to complain, and I was livid.
We got back all of our damage deposit, but I still say the problem was horrible and uncalled for. We never got rid of it.
You can try kabi-killer, vinegar, plain old soap and water, whatever. Rags or brushes. It just doesn't help because it's in the walls or floorboards, where (I believe in my heart) there is little to no insulation, and that THAT may be the chief cause). People talk about ventilation (raising boxes in your closets, for example) and using those boxes of gel to absorb moisture, but none of that helped us. We threw away clothes that hung in the open and that were in boxes, even though we had the closet doors open all the time and the dehumidifier running next to the closet.
My only question is, why isn't there mold in the storage lockers? Perhaps less warmth/humidity from the apartment life (cooking, shower vapors, body heat). One can't live in a storage locker, though.