This is from ehow.com. May answer all of your questions…why? and how to fix.

Looks like water based paints do not work over nicotine. Maybe that is the issue right there.

Good luck and congrats on being cigarette free.

Take note of the ventilation warning. You or your painter will need a mask.

Proper preparation of the surface is essential to a quality paint job. Since the greasy nature of nicotine stains will prevent paint from adhering to the surface, use a degreasing agent to clean the ceiling. Trisodium phosphate (TSP) is a powerful degreaser commonly used by professional painters to remove stubborn stains caused by nicotine, mold and mildew. TSP is an extremely strong chemical. Be sure to wear protective clothing and eyewear to prevent skin and eye irritation.

Primer
Because nicotine stains tend to bleed through paint, it is important to prime your ceiling with a stain-blocking primer. Pigmented shellac and oil-based primers provide a good barrier between stains and paint to prevent bleeding. Water-based primers are not effective with water soluble stains and should not be used on nicotine. Many primers have a strong odor, so use only in a well-ventilated area.


Paint
Once your ceiling has been primed, you may choose to finish with latex or oil-based paint. Latex is a frequent choice for do-it-yourselfers due to its easy application and cleanup. Because of its high water content, latex is a more eco-friendly choice than oil-based paint. Oil-based paints are stickier and require more dry time than latex paint. One of the chief advantages of oil-based paint is its ability to adhere to dirtier surfaces than latex. However, since your surface is cleaned and primed, this is not an issue.

Textured Ceilings
Stained textured ceilings present a couple of challenges. Popcorn, or acoustical, ceilings cannot be cleaned with water, and ceilings installed prior to 1980 may contain asbestos. This is generally not a safety hazard as long as the surface is not disturbed. While you cannot use a water-based cleanser on your popcorn ceiling, it is important to remove as much dirt as possible. Use a vacuum cleaner to remove loose dirt and cobwebs that form in the textured nooks and crannies. If you are absolutely sure your ceiling does not contain asbestos, you may use a paint roller with a roller cover designed for textured surfaces to prime and paint the ceiling. If you suspect asbestos, use an airless paint gun to apply the primer and paint.

Check to see if the fan is actually vented to the outside.

I don't have a popcorn ceiling and the nicotine and mildew/mold is on the painted walls. Everyone is talking about my ceiling, so I had to go back and see if I had mentioned it. I am talking about my walls and the beaded board. The mildew is on the walls and so is the nicotine. After I clean with TSP, I was asking about any special primer and any special paint, such as semi-gloss, instead of flat. Yes, the fan is vented to the outside. My ceiling is not affected at all.

Sorry I didn't make myself clear.

Strip the paint above the beadboard. Wash with TSP and rinse thoroughly. Prime with oil based primer. You may need a couple of coats. Paint with oil based paint to which mildew preventer has been added. See your paint store for help. Follow instructions carefully.

The mildew and dripping problems indicate that the fan is not exhausting fast enough to keep condensation to a minimum and to keep mildew from growing. You may need to run a portable fan off a GFCI outlet or put the exhaust fan on a timer that runs 15 minutes after the shower ends or use an exhaust fan that is activated by a humidity level (more expensive). You can also put in a fan that exhausts more air at a faster rate.