Forbidden Mixtures

Following up on a discussion in the comments section about whether one can merely look at the ingredients of an item and determine whether it is kosher, I present the following sources. This is not intended as a well-researched or thorough post. I just pulled some stuff together after dinner.

Regarding whether something that one cannot taste is permissible to eat, there is a three-way disagreement among rishonim about whether something is forbidden if one cannot taste it but it is more than 1/60th of a mixture. The Rema rules strictly like Rashi, the Ramban, the Rashba and the Ran. On this, see Arukh Ha-Shulhan, Yoreh De'ah 98:21-22, 25.

R. Akiva Eiger (Glosses to Yoreh De'ah 99:5) quotes a responsum of the Rivash to the effect that someone manufacturing a foodstuff who dilutes a forbidden ingredient is diluting it on behalf of all of his customers and the mixture is therefore forbidden to anyone who buys it. This is, however, hotly disputed. The Darkhei Teshuvah (99:67, 108:20) quotes a host of posekim agreeing with R. Akiva Eiger and a host disagreeing with him. The rabbi who taught me Yoreh De'ah agreed with R. Akiva Eiger.

The upshot of these two positions is that if a manufacturer mixes a forbidden ingredient into food to the point that one cannot taste it, the mixture is forbidden to all.