When you feed your sourdough starter, you discard most of it and supply fresh flour and water. This sets up ideal conditions for growth. The yeast is faster to grow than the bacteria, so the ratio of yeast to bacteria is higher immediately after feeding. Thus, you can control the sourness of the dough through those feedings and their timing relative to preparing the final bread dough.
The microorganisms should be invisible. You just see their effects on the mixture. Your starter is probably good if it doubles in size within a few hours of feeding (due to carbon dioxide production by the yeast). If there's visible mold, that's very bad. The yeast should be strong enough to defeat any stray mold long before it can grow enough to be visible. I would just throw that batch out and start from scratch.
Yeast is a fungus. Sourdough bread has always been described to me as "natural yeast", which I assumed was a fungus microorganism.
EDIT: Seems like Sourdough Type I has Saccharomyces exiguus, Candida milleri, or Candida holmii as its fungus. Perhaps it isn't "Mold", but those aren't bacteria either. In any case, the ancient, or even middle-ages cook, wouldn't have known about these different microscopic microorganisms when they created sourdough, cheese, or yogurt.
The growth of Lactobacillus is still important apparently for sourdough. In any case, the idea of micro-organisms changing the taste (for the better) of various recipes would have been discovered by the first baker of leavened bread, a truly ancient discovery. Yogurt and Cheese are simple extensions of the principle.