Zorro:
Certainly, having a fan to keep the room dryer that it otherwise would be will help a lot.
To remove the mildew semi-permanently from the tile grout, read and follow the directions posted by me in this thread in the Painting and Decorating forum:
"Tile Grouting" posted by russellm72 on Monday, January 23, 2006 with last post on Sunday, January 29.
As for the other surfaces, clean the mildew off of them (perhaps with a bit of bleach) and then use a spray bottle to spray some undiluted bleach onto those surfaces and let it dry there. If you find that doing that doesn't help very much then proceed as follows:
1. Phone around to the paint stores in your area and see which of them sell packets of mildewcide that can be added to paint to prevent mildew from growing on that paint.
2. Also, go down to that paint store and buy the smallest can of water based "varnish" they have. Alternatively, perhaps use a quart size can of EXTERIOR emulsion paint in the deepest tint highest gloss base it comes in. (A deep tint base is one which has the most room in the can for adding colorants. Such tint bases will dry to a transluscent film if not tinted to the desired color in the paint tinting machine.)
What I'm suggesting is that you add the mildewcide powder to clear drying water based high gloss "varnish" or a deep tint high gloss exterior (or interior paint) and paint that on the problem areas and let dry.
Mildewcides work because they're soluble in water and their affinity for water causes them to migrate through the paint film to it's surface when that surface is wet. This migration process is called "leeching". The mildewcide is washed off the surface of the paint film by the shower water, but the mildewcide that dries up on the surface after the shower is over will kill any mildew spores before they have a chance to grow.
However, the gloss level of the paint has a pronounced effect on how quickly the mildew can migrate to the surface of the paint. The higher the gloss of the paint, the more slowly the mildewcide moves to the surface where it'll be washed off by the spray water, and the longer the surface will remain mildew free.
On the other hand, if the mildewcide migrates TOO slowly through the paint film, it might not come out in sufficient quantity to be effective in controlling mildew.
Consequently, what you may have to do is stick something (like a sample of plastic laminate) up in your shower with double sided tape (or whatever) and paint it with mildewcided treated emulsion paint or mildewcide treated water based "varnish". Once the mildew starts growing on that plastic chip, add some more mildewcide to your quart can, shake it up, and paint that onto the surface of the laminate chip.
By doing that, eventually you'll reach the concentration of mildewcide in the emulsion paint or water based varnish that will leach out of the film at a fast enough rate to be effective at controlling mildew. Then, keep adding mildewcide to that water based paint until it becomes detrimental to the transparency of the dry film the paint dries to.
Then, paint that stuff onto the problem areas.