No paint company would ever recommend painting a wall that hasn't been cleaned first, even though lots of people consider repainting an alternative to cleaning.
You should clean the dust off the walls. Trust me on this: You're a lot better off cleaning the walls before painting them than you are dealing with paint that's cracking and peeling on the walls because it isn't sticking. Once you paint over a dirty wall, the dirt is much harder to remove and if it causes a loss of paint adhesion, that problem is going to be a permanent one.
What you should do is:
1. Buy a half dozen to a dozen Magic Erasers and clean the walls with them everywhere except the kitchen and bathroom if the house wasn't occupied by smokers. You don't need to use a cleaner in the other rooms; just get the Magic Eraser wet with water and go to it. The Magic Eraser will clean the walls well, and it's also about the best cleaner for removing marks from walls that you can buy. So, you can clean both the walls of dirt and marks at the same time.
Ceilings can be cleaned with a sponge mop in most cases. The only place you really need to use cleaners is in the kitchen and bathroom.
2. In the kitchen, clean the walls and ceilings with a Magic Eraser using Mr. Clean (or Simple Green), and then rinse the cleaner off the walls with a sponge and clean water. You see, cooking grease will accumulate on the kitchen walls and ceiling, and that can interfere with paint adhesion. Similarily, you need to use a bathroom cleaner (like Scrubbing Bubbles or a very mild acid, like a 5 to 10 percent phosphoric acid based bathroom cleaner or toilet bowl cleaner to cut through any soap scum accumulated on the walls and ceilings in the bathroom. Soap scum will also interfere with paint adhesion.
3. To check for paint adhesion, simply stick some painter's masking tape to your walls and ceiling prior to painting. Pull the painter's masking tape off, and if it pulls off with about the resistance you'd expect, then the surface is good for painting. If the painter's masking tape pulls off more easily than you'd expect, there's something on that surface that needs to be cleaned off because it's interfering with adhesion.
My experience has been that cigarette smoke is relatively easy to remove because it's soluble in water. However, because it sticks to everything, you have to clean everything (including doors, windows, ceilings, curtains, carpets, etc.) to get rid of the smoke smell in a house or apartment. Also, most of the cigarette smoke will come off with water, but to get the walls really clean the way they should be, you also need to wash them down with a dilute bleach solution (bleach diluted 10:1 with water). The bleach will both remove the smell and discolouration of the paint caused by the smoking.
TSP is something that's commonly recommended for cleaning walls before painting, because TSP will dull the gloss of OIL BASED PAINTS. Doing that greatly increases the surface area of the old paint, with the result that the new paint sticks better. However, TSP only dulls the gloss of oil based paints. It has no effect at all on latex paints. So, if you know your existing paint is a latex paint, you're much better off using a better cleaner like Mr. Clean than you are using TSP. If you're existing paint is an oil based paint, then you're much better off using TSP than Mr. Clean because doing so will improve the adhesion of the new paint (because it can grip a larger surface area).
Walls and ceilings cleaned with either TSP or any cleaner should be rinsed with clean water and given time to dry before painting with either oil based or latex paint.
Also, when painting the bathroom, always use a paint MEANT for bathrooms. It's so often that people complain about paint peeling in the bathroom, and this is often misdiagnosed as poor preparation prior to painting. Most of the time, however, it's simply because lower priced vinyl acrylic paint was used in the bathroom. Vinyl acrylic paints use a binder made from polyvinyl acetate, and this plastic will loose it's adhesion in damp or humid conditions. Buy a paint specifically meant for bathrooms like Zinsser's PermaWhite Bathroom Paint to avoid paint problems in your bathroom. (But, even Zinsser's PermaWhite needs a clean surface to stick well to.)