Gemara

42a (Mishnah): The following are Ovrim during Pesach (one transgresses for them, or must remove them): Kutach of Bavel (a dip made with stale bread and whey), beer of Madai, vinegar of Edom... and Kolan of Sofrim (glue or a salve);

R. Eliezer adds women's cosmetics.

The general rule is, during Pesach, one transgresses for anything from grain. There is a Lav for it, but not Kares.

43a - Question: Who is our Tana, who forbids both Nuksheh and mixtures of Chametz with a Lav? (Nuksheh is grain that started fermenting, but never became proper Chametz that is good to eat.)

Answer #1 (Rav Yehudah): It is R. Meir. He forbids Nuksheh with a Lav. All the more so a Lav forbids a mixture of [proper] Chametz!

Answer #2 (Rav Nachman): It is like R. Eliezer:

(Beraisa - R. Eliezer): One who eats proper Chametz is Chayav Kares. One who eats a mixture of it transgresses a Lav;

Chachamim say that one who eats a mixture does not transgress anything.

R. Eliezer forbids a mixture with a Lav. All the more he forbids pure Nuksheh with a Lav!

Support (for Rav Yehudah - Beraisa): "Kol Machmetzes Lo Sochelu" includes Kutach of Bavel, beer of Madai, vinegar of Edom, and Zeisum ha'Mitzri;

"Ki Kol Ochel Chametz v'Nichresah" - one is Chayav Kares for pure Chametz, but one transgresses [only] a Lav for mixtures.

We know that R. Eliezer forbids mixtures with a Lav. [Surely, the Beraisa is like him, and] he does not teach a Lav to forbid Nuksheh!

Rishonim

Rif and Rosh (13a and 3:1): Rabanan say that one does not transgress at all for a mixture. I.e. one is not lashed, but it is forbidden. They exempt from lashes when there is not k'Zayis of Chametz bi'Chdei Achilas Pras (in half a loaf, i.e. three or four eggs, of the mixture). If there is k'Zayis bi'Chdei Achilas Pras, Chachamim agree that one is lashed.

Rosh (ibid.): The Rif explained Chachamim. This implies that he rules like them. Even though our Stam Mishnah is unlike them, he does not consider it [authoritative like a] Stam Mishnah, because there is a later Mishnah (48b) unlike R. Meir regarding Sei'or [an early stage of Chimutz, which is Nuksheh]. Therefore, our Mishnah is like a Stam followed by an argument regarding Nuksheh, so also for mixtures it is not Stam.

Rambam (Hilchos Chametz 4:8): One transgresses Bal Yera'eh and Bal Yimatzei for a mixture of Chametz such as Muryas (fish oil with flour), Kutach of Bavel, beer of Madai that they make from flour, and all such foods.

Rambam (12): Something in which Chametz was mixed, and it is not a food at all, or most people do not eat it, even though one may keep it, one may not eat it until after Pesach, even if it has only Mashehu of Chametz.

Rosh (ibid.): R. Tam holds that one does not transgress Bal Yera'eh for a mixture. According to the reason (Tosfos 2a DH Ohr) that one must do Bi'ur and not rely on Bitul, because he does not normally refrain from Chametz, and he might come to eat it, one may not keep the mixtures in our Mishnah. However, if the Chiyuv Bi'ur is because one who does not do Bitul transgresses Bal Yera'eh and Bal Yimatzei, according to R. Tam one may keep them.

Tosfos (42a DH v'Elu): Rashi explains "Elu Ovrin" to mean that one transgressed Bal Yera'eh and Bal Yimatzei for these [mixtures and Nuksheh]. Also Riva explains that they pass from the world. R. Tam disagrees. We needed a verse to teach that there is a Lav for mixtures! What is the source that Bal Yera'eh and Bal Yimatzei apply to them?! Rather, they pass from the table, i.e. one may not eat them.

Poskim

Shulchan Aruch (OC 442:1): One transgresses Bal Yera'eh and Bal Yimatzei for a mixture of Chametz such as Muryas, Kutach of Bavel, beer of Madai, and all such foods.

Beis Yosef (DH u'Mah she'Chasav Af): We find that R. Shimon is lenient about Chametz she'Avar Alav ha'Pesach that was mixed afterwards. However, he is not lenient about Chametz that became mixed before Pesach, to keep it during Pesach. He is lenient only when it became mixed after Pesach. Since the quantity increased over the amount at the time of the Isur, he does not fine [to forbid it]. If it became mixed before Pesach, the one who forbids keeping it during Pesach holds that it is still forbidden after Pesach. Since the quantity did not change, he fines him. If so, we cannot learn a Heter to keep a mixture of Chametz during Pesach from the lack of a fine for Chametz she'Avar Alav ha'Pesach that became mixed.

Beis Yosef (DH u'Matzasi): In some texts of the Tur, it said "this is only when it became mixed before Pesach', and Talmidim erased it and wrote 'after Pesach.' It seems that we must correct the text like this. If he does not fine when it became before Pesach, all the more so if it became mixed afterwards! Also, if it became mixed beforehand, and there was not 60 times as much Heter, he was obligated to do Bi'ur. Since he did not destroy it, it is proper to fine him, like the Magid Mishneh says. If this was the Tur's intent, he should have distinguished between when it became mixed. Rather, he said that when the Chametz is intact, it is more severe. This connotes that he holds that there are two kinds of mixtures. One is when it became mixed without intent. The other is when it is intentionally mixed, e.g. Kutach. R. Shimon does not fine in the first case, even if it became mixed before Pesach. If he intentionally mixed in Chametz before Pesach, this is more severe. We need not alter the text of the Tur.

Beis Yosef (DH u'Mah she'Chasav Rabeinu): The Tur says that Rabanan, who hold that there is a mere Isur [on mixtures] without a Lav, permit keeping it. This is astounding. It seems that Chachamim agree that there is an Isur Torah. If not, they should have taught "a mixture is permitted"! Also the Tur connotes like this. Since the Torah forbids eating it, why may one keep it during Pesach?! Perhaps he learns from the Rosh, who says that according to R. Tam, if the Chiyuv Bi'ur is due to Bal Yera'eh, one may keep mixtures. However, he should have explained himself, for if Bi'ur is due to concern lest one eat it, one may not keep them.

Beis Yosef (DH Matzasi): Why does the Tur say that R. Eliezer holds that there is a mere Isur for keeping them? The Rambam says that there is Bal Yera'eh! The Tur holds like Tosfos. The Rambam holds like Rashi.

Magen Avraham (1): The Tur and Semak say that anything the Torah did not forbid to eat, l'Chatchilah one may mix it and keep it. Tosfos (2a DH Ohr) says that Chachamim did not distinguish. They prove this from Sei'or. Even though it is Nuksheh, and the Torah does not forbid eating it, and all the more so tt6 does not obligate Bi'ur, mid'Rabanan one must burn it. The Ran says so. The Tur must say that the case of Sei'or is on Yom Tov, when one cannot bake it, since mid'Rabanan one may not eat it. If he will leave it, it will become total Chametz. Therefore, he must burn it. The Shulchan Aruch holds that Tosfos, for in 447:12 he rules that one does not transgress Bal Yera'eh mid'Oraisa for Nuksheh. This shows that he holds that there is no Lav against eating it, for he rules like the Rambam and Rashi, and like Rav Yehudah, for the Beraisa of Machmetzes supports him. (It did not mention Nuksheh.) This implies that Nuksheh is not included in the Lav "Lo Sochlu", like the Stam Mishnah that exempts for eating Sei'or. Even so, he forbids keeping sei, but if one kept it, one may benefit from it, since he did not transgress Bal Yera'eh. Regarding a mixture, the Shulchan Aruch rules like the Stam Mishnah, according to the Rambam.

Mishnah Berurah (4): The Acharonim agree that whiskey, which is made from grain, is total Chametz. It is worse than a mixture.

Kaf ha'Chayim (12): Beis Hillel (the Posek) says that even though whiskey is merely a sweat (secretion) from grain, it is like Chametz itself.

Kaf ha'Chayim (14): If there is a Safek that wheat fell into wine, it is Kosher even for the four cups. If wheat was found in oil, one should not light the oil during Pesach.

Shulchan Aruch (ibid.): One may keep a mixture of Chametz improper to eat, e.g. an eye-potion, bandage..., for they lost the form of Chametz.