I am also seeing tiny white bugs that I think are mites. The are small as a pinpoint and they crawl all over the surface of the soil, and sometimes on the leaves, but they don't appear to be feeding on the leaves. I think they are just predatory or soil-eating mites which will not be bad at all, in fact they will either compete against bad guys or eat the bad guys. I figure if you don't see any damage to the plants, the chemicals and soaps will be more harmful than the bugs. Honestly it gives me comfort to know that the soil I'm using can support living things.

Spider mites leave little webs all over the leaves, and they drop sugar which leads to mold infestations. Aphids also leave sugar everywhere. Both are easily recognizable.

One thing I do see is fungus gnats, but I haven't noticed any damage from them. Maybe they are impeding the growth of my plants? Could they be causing yellowing and necrosis of the lower leaves? Maybe if they are doing so much damage to the roots. But they usually don't damage established plants, only seedlings.