Wine typically only has two ingredients, grapes and yeast, neither of which are unkosher. So why does the Star-K Kashrut authority call kosher wine production “one of the most sensitive, tedious, and difficult processes to oversee”?
Because of idolatrous worship.
The relevant Torah passages describing idol worshipers come from Deuteronomy 32:32: “For their vine is of the vine of Sodom, and of the fields of Gomorrah: their grapes are grapes of gall [poison], their clusters are bitter.” This has been interpreted as saying that kosher wine cannot be touched by non-Jews during any stage of production or bottling, or after the seal of the bottle has been broken. Of course, production is strictly supervised by rabbis to ensure that these conditions are met.
But according to the Chabad website, wine can be boiled to make it “unfit” for idolatrous sacrifices. This wine is called yayin meshuval, and can be handled by non-Jews.
Wine Spectator writes that producers are now embracing flash-pasteurization techniques which can heat wine and cool it down almost immediately, guaranteeing meshuval status while minimally affecting the wine’s flavor.
To make matters more complicated, traditional Concord kosher wine is often sweetened with corn syrup, which is not kosher for Passover for many Jews. Kosher for Passover wine must be certified to not contain any such additives and to have been produced with equipment that has not touched such ingredients, in addition to the standard laws for kosher wine.