I need help with this as wel.
What kind of patches? Can you post a picture?
Mostly ceiling issues are related to mildew. Best is to spray a mildew-killer allow to dry, wash it off and repaint the ceiling with an appropriate bathroom ceiling paint. Contractor's cheap paint is no good.
If you are talking about stains then you need to paint a primer, Zinsser Bullseye 1-2-3, over the whole ceiling and then use a good quality paint to cover.
Mildew(black powder)is what we have in the bathroom ceiling, manly above & around the bath/shower area and above the window !