How can I fix this patchy paint job?
If you're sure the wall itself is flat and there's no major paint drips/lines on it, you could try another coat on one of the walls and see if that makes a difference. I can't really tell if there is just a difference in sheen on your walls or if there are surface issues.
Also, The less shiny the paint, the less obvious the imperfections when light hits it.
I wouldn't ever try sanding wall paint. Depending on the paint, it can peel off like a sunburn from the heat of the friction if there are drip lines. If there's major surface issues, you could mud over it and sand it down to re-smooth wall. I also personally wouldn't water down the paint.
Just my opinion... we'll see what others say. ;)