I sold paint for years and the number one reason for a crappy paint job is not washing the walls. I know people will tell me they do it all the time however you must wash the walls (i use tsp) and then rinse.Take a look at the water and tell me that the paint will stick well. If you have ever painted and the paint kinda smears dont blame the paint. Its the grimy greasy crap on the walls. Sorry to say there is nosubstitute for washing the walls.
But I wish there was…
Spray down with bleach and water solution. Rub any scuffs with a towel after spraying. You’ll have to close the door and leave the room for a bit after spraying it, but it works well- especially on flat white walls.
TSP does a very nice job of cleaning walls, IME. As to blending in the patches, yeah, you’re in for a struggle with that – I find it’s much more effective to just paint the whole wall rather than try to touch up a patched spot and it gets harder as the walls age.
Well, I’m sure that’s the “best” way to do it, but I have my walls professionally painted and they wipe them down (to get rid of dust) but they never actually wash them. The paint always sticks…even the colors I don’t like much. 
yeah know, one pro painter told me he gets paid to paint, not to clean. When id go to the factories for looksee and training they would complain about it all the time. The best paint job comes with washing the walls. Seems a bit silly to spend 35 bucks a gallon on paint and not to do prep work. Goto your kitchen and wash half the wall with tsp. Shocking difference eh!
When my son moved out and into a condo where smokers used to live we spent a long weekend washing walls. They needed 3 washes and the dirty water smelled like old butts! yikes…
so walls get dirty and need a wash. pretty simple.