Completely agree with the tobacco theory. I had this in my last apartment where I lived for 16 years and I smoke.
After a shower or bath and the room is somewhat humid yet, I would take a sponge mop with a drop of bleach added and simple sponge the walls down. You may have to repeat it a couple of times, but it will eventually disappear.
said by ErikRP:My money is also on tobacco/smoke tar. We had it in our house, the former occupants smoked.
(Not to give an anti-smoking commercial, but if it's that hard to get off your walls, imagine a smoker's lungs...)