Those unsightly blotches are mildew caused by humidity in the bathroom. Kill it with a standard bleach-containing bathroom cleaner (which thou shalt not mix with Windex, as per Skill No. 21), then prep the ceiling and repaint it. Prime with a sealer primer, such as Kilz, to cover the stain. Finish with a premium bathroom paint that contains a mildewcide to prevent any new growth. Then, let your vent fan run for 20 minutes after every shower.