Fungal problems have been common in my garden room. Humidity and a lack of air exchange are most likely the problem. This article from Associated Environmental Consulting Group goes into further detail about mold and fungus problems in greenhouses. Controlling Mold In Greenhouses - Catalogs.com offers advice for greenhouse control.
Here is a safe and natural product which I have not used but looks promising.
Jon Parr has also taught me to use H2O2 (Hydrogen Peroxide) I now keep a spray bottle filled and handy at all times. It's great for sanitizing tools and seedlings. Yep a 3% solution is safe for your plants, you and any fish you may have. Of course I'm talking about small amounts sprayed on your plants. H2O2 converts back to H2O and O very quickly.
Jon Parr and Vlad are some of the best contributors to the aquaponic forums.
Here's a little advice they have pasted on that I appreciate.
Link to discussion
GH (Green House) pest management has three strategies, and which is best is really open for debate.
1- intentionally low pest security, meaning wide open large screens for honey bees, pests, and pest predators. This works pretty good for lazy folks like myself, especially if you are planting beneficial plants to attract the predators. No fuss about pollination, and no big concern about sterilizing everything.
2- moderate pest security. This one is fine for new greenhouses, and light traffic GH's with cleanly guests. Once a pest gets inside, though, trouble trouble.
3- high security, meaning positive pressure and HEPA filters, thrips screening, humidity and temp control, haz-mat suits and dissinfect routines. Just the thought of all that work spoils my mood, but is probably the smartest long term plan for commercial use.
I'm a low security type guy. Address the pest directly. Mold? Increase airflow and temp, decrease humidity. Spider mites, fungus gnats, white flies, aphids? Allow predators, spray with tea, nuke them with CO2. Nasturtiums are awesome for the garden by the way; trap crop or aphids, pest predator magnets, repel white fly and spider mites. Yep. And borage, and multicropping.
Link to discussion.
You can use the 'ol 3-5% oil + 0.5% dish washing detergent remedy...works well but you have to be real careful to get as little of the concoction into your system and take measure to cover up your fish tank to protect from overspray. And even this low % of oil will burn pepper plants if you have any...won't damage them beyond repair or anything, just don't be freaked out by the necrotic lesions that will be left on their leaves. peppers seem especially sensitive to this type of treatment.
A better/easier/more fish safe bet might be a naturally occurring fungus called Beauvaria bassiana that will take care of a whole host of common garden pests...spider mites included (and then some). B. bassiana can be purchased under the trade names Botaniguard, Naturalis-L or Mycotrol-O the later two being ok'd by OMRI...and more importantly it is fish safe (unlike any kind of oils or most soaps).
Whatever you spray with make sure to repeat after 3 or 4 days...then again after 3 or 4 days...and then once more...since most of these sprays wont kill the eggs that they've laid...so make sure you get the bastards that have hatched...and spray the under-sides of the leaves...Good luck. Spider mites are a royal PITA.