Yes, your trays need to have drainage holes. I would put lots more drainage holes and then flood your trays several times a day with water and see if that takes care of the mold.
I have been growing both barley and wheat fodder. I started off with some major mold problems especially when I used barley. I bought a big bag of both at the feed mill and the barley is supposed to be cleaned but it has all kinds of other stuff in it while the wheat has just wheat. In an attempt to prevent the mold, I do the following things. In the initial soak, I add about 1 Tbls of Oxine (without the activator). It is safe to put in bird's water, to use as mouth wash, etc. so I feel comfortable using it on my fodder. I soak the seeds for 8-12 hours, drain, rinse a couple of times, and let them sprout in the same container for 2 days making sure to rinse at least twice a day. Then I spread out the seed in a tray with holes making sure that they are only about 3 seeds deep. I put that tray in another tray without holes and cover it with another tray. I rinse the seeds with cold water 3 times/day for 3-5 min. per rinse. Rinsing more often for longer periods and having fewer seeds has helped prevent the mold. I also sometimes spray the sprouted seeds with a diluted Oxine mixture to take care of any surface mold spores. I leave the tray covered until the sprouts are 1/2-1 in. tall. Once I remove the cover, they green up within a day. With the barley, I have been feeding it to my birds when it is 1-2 in high and before the roots start getting mold on them. The wheat, I can let grow higher because I rarely have a mold issue with it. I'm not sure if I just got a bad bag of Barley but it also causes problems in my fermented feed. I have started sprouting it and then planting it in soil in outdoor trays with hardware cloth covers. It grows up and my girls eat it through the screen. It lasts for months that way.
