Green or white fuz spots on the surface  
of the log:  This is a green mold which
usually forms on the log in a commercial
growing environment.  If you see this
scrape it off and spray a very light
mixture of bleach/water all over the log.  
Green mold forms because of too much
humidity, so you may want to cut back
on the watering a little and take the log
out of the tent.
The white stuff you see are spores dropping from
the mushrooms.
Tanins in the soaking water from the
sawdust in the logs.