The issue of whether dental products require a Hechsher (rabbinic kashrut certification) is hotly debated. Since they are not food items, and therefore not subject to the laws of Kashrut, many authorities ridicule or scoff at the idea that dental products would require a Hechsher. Yet there are still a significant number of Poskim who believe that dental products certainly would require a Hechsher, because toothpaste and mouthwash do contain ingredients that can be considered to be food. One of them, glycerin, is not kosher. Therefore, perhaps toothpaste and mouthwash would require a Hechsher to clarify that they do not contain any glycerin.
However, the question remains as to whether the glycerin is rendered Nifsal, inedible, due to being mixed with the other non-food ingredients. Non-kosher food that has become inedible, or “Aino Raui Le’Achilat Adam,” “not fit for human consumption,” is permitted to be consumed. Therefore, even though toothpaste and mouthwash contains glycerin, a Hechsher is not required since the glycerin was Nifsal. However, Rav Yisrael Belsky is of the opinion that since toothpaste and mouthwash include flavoring, the glycerin is not considered inedible. Therefore, toothpaste and mouthwash do require a Hechsher. But would toothpaste and mouthwash still require a Hechsher even though they are spat out, and not consumed? Rivash (Teshuvot No. 288) writes that, indeed, there is a rabbinic prohibition to taste non-kosher food even with the intention of spitting it out.
Interestingly, the source for this rabbinic prohibition is unclear. The Rivash discusses a potential source. He begins by writing that perhaps it emerges from the Gemara’s discussion of “Te’im’at Kefaila”, the non-Jewish cook who tastes food. If non-kosher food falls into kosher food, in order to determine if the non-kosher food is “Bateil”, null and void, a non-Jew chef may taste the mixture to determine if the taste of the non-kosher item is distinguishable (Shulchan Aruch Yoreh Deah 98:1). Had Halachah permitted a Jew to taste non-kosher food, a Jew could simply taste the mixture, and involving a non-Jew would not be necessary. Accordingly, we see that a Jew cannot taste non-kosher food even in a “Safeik,” doubtful situation. Moreover, this may not pertain to the case of dental products, because it is a case of tasting and swallowing. In such a situation, it is certainly forbidden for a Jew to taste the food.
The next source that the Rivash quotes is the Gemara (Avodah Zarah 66b), which discusses a case of smelling non-kosher wine with one’s mouth. Abayei prohibits it and Rava allows such an action. The Rivash explains that Rava only allows smelling the wine, but tasting the wine, even if you spit it out, is not permitted. The Rivash mentions that this source could be rejected as a proof because non-kosher wine is treated more stringently than other non-kosher foods, with the exception of meat and milk. This is shown by non-kosher wine’s Issur Hana’ah (prohibition to derive benefit) which does not apply to other non-kosher foods. Thus, perhaps only non-kosher food upon which devolve an Issur Hana’ah cannot be tasted, but we are permitted to taste other non-kosher foods, provided that you spit out afterwards. However, the Rivash asserts that the Gemara refers to all non-kosher food, and is not limited to Issurei Hana’ah. The Rama (YD 108:5), the Shach (YD 108:24), and many others, agree with the Rivash and write that the prohibition includes all non-kosher food. Therefore, according to those who argue that toothpaste and mouthwash are foods, they must be kosher and require a Hechsher, even though one has the intention to spit them out.
In contrast, those who say that dental products are not considered food, would not prohibit using them without a Hechsher. This, however, may not be the case. There is a rabbinic prohibition against eating Nifsal food, called Achshavai (Rosh Pesachim 2:1, Shulchan Aruch Ohr Hachaim 442:9, Taz 442:8, Mishna Berurah 442:43). Achshavai is food that is objectively spoiled, but if a person chooses to eat it, he implies that on a subjective level he considers it to be food. The Rabbis forbade the consumption of non-kosher items in such a scenario. If there is a rabbinic prohibition of eating Nifsal non-kosher food then perhaps there is a prohibition of tasting non-kosher, Nifsal food.
The Responsum Tzemach Tzedek (47), Rav Menachem Mendel Krochmal of Nikolsburg, in response to a question regarding soap tasting, writes that there is no prohibition of tasting Nifsal non-kosher food. He was asked if a Jew was allowed to taste the soap to make sure there was enough salt, even though it contained non-kosher fats amongst the largely non-food ingredients. The Tzemach Tzedek ruled leniently since tasting and spitting out real non-kosher food and eating non-kosher Nifsal foods are both rabbinic prohibitions, and we do not combine the two to create a new prohibition. The Pitchei Teshuva (Yoreh Deah 98:1) quotes this ruling of the Tzemach Tzedek. According to this Teshuva, toothpaste and mouthwash should be permitted without a Hechsher.
However, the Noda BeYehudah (Yoreh Dei’ah Tinyana 52) disputes the opinion of the Tzemach Tzedek. He quotes the Tzemach Tzedek’s son who states that all foods that are rabbinically prohibited to eat are also prohibited to taste, contradicting his father. The Noda BeYehudah brings a proof from the Rama quoted earlier. The Noda BeYehudah notes that the Rama distinguishes only between a Biblical prohibition, Yayin Nesech and a rabbinic prohibition, Stam Yainam. But the Rama does not distinguish between forbidden wines and foods, because you may not even taste the foods.
The Rivash explained that tasting non-kosher food is prohibited because they may inadvertently swallow a little bit of the food “and violate a biblical prohibition.” Therefore, maybe we could postulate that the Rivash only prohibits tasting if it might cause a biblical violation but not a rabbinic prohibition.
Rav Tzvi Pesach Frank (Har Tzvi Responsum 95) is lenient and does not require a Hechsher on toothpaste. He notes that the Rivash prohibited tasting food because someone may come to consume some of the forbidden items. Therefore, one can suggest (despite the wording of the Rivash) that we should even be concerned about swallowing foods that are biblically prohibited. However, one is not allowed to eat Nifsal foods because of “Achshavai”. The person eating the inedible food subjectively considers this spoiled food to be consumable. Toothpaste, however, has an unpleasant taste, and therefore nobody considers it to be an edible food. Rav Herschel Schachter explains that Achshavai applies only when the individual has intent to eat it as food. With regards to toothpaste, the issue is accidentally swallowing something, so Achshavai does not apply (Mishna Berurah 442:45) Furthermore, the Mishna Berurah (442:43) and Chazon Ish Or Hachaim (116:8) write that Achshavai does not apply when the Nifsal item is mixed with other items. Therefore, if toothpaste and mouthwash are not considered food, they should not require a Hechsher.
However there are some who clearly disagree even with this distinction. The Peri Chadash (108:22) vehemently disagrees with the Tzemach Tzedek. He believes that when the Rabbis prohibited eating certain types of food, they forbade even tasting the food. For instance, the prohibition against eating Nifsal food also included tasting such items. Additionally the Peri Megadim (MZ 98:1) argues that tasting food is not rabbinically prohibited but Biblically prohibited. He quotes the Gemara (Chullin) which discusses where the prohibition of actualizes itself, in the stomach or the throat. Since we answer that it is the throat, if the throat receives any benefit, the prohibition has been violated. The Rambam (Machalot Asurut 14:6) writes that any food stuck in the gums constitutes the volume necessary to violate the prohibition. The Peri Megadim states that therefore any non-kosher food in the mouth is considered as if it is providing Hana’ah, benefit, to the throat and is considered a biblical violation. If the Peri Megadim is correct that one of the prohibitions is biblical in nature, then the entire leniency of the Tzemach Tzedek vanishes (since it was predicated upon having two rabbinic prohibitions). Also, the rabbinic prohibition would be patterned after the biblical ones, so food automatically providing benefit to the throat also applies to the rabbinic prohibitions.
There may be another reason to argue that the Kashrut of toothpaste involves a biblical prohibition. This whole discussion is presupposing that the proper way to brush teeth is to brush and spit out the toothpaste. But there have been relatively new instructions for brushing teeth, especially for those who experience many cavities. One should brush their teeth, but leave the toothpaste to allow the fluoride to absorb into the teeth. If this is the case then the concern is no longer just in the realm of tasting, but it is very likely that minute amounts of toothpaste will be swallowed. Therefore, according to those who say these items are food, brushing with toothpaste would no longer be a rabbinical concern but maybe a Biblical concern. Also, the Tzemach Tzedek’s leniency would not apply for those who are lenient and hold that these items are not food, then, and one would need to rely on Rav Frank and Rav Schachter to allow for leaving the toothpaste on one’s teeth overnight.
 Avodah Zarah 67b-68a
 https://oukosher.org/blog/consumer-kosher/kashruth-issues-of-toothpaste/, Opinion of Harav Yisroel Belsky Shlita as expressed in OU document I-98 page 2.
 The Rama adds that nowadays we don’t rely on the tasting of the non Jew but on the measurement of “Shishim”, nullification in sixty parts. If there is sixty times more kosher food than non-kosher food the non-kosher food is Bateil. The Kaf HaChaim and Rav Ovadia Yosef write that Sephardic Jews also follow this Rama.
 Not all Rishonim agree that it is a case of smelling with the mouth.
 See the Kaf HaChaim 108:63 for a list of these authorities.
 The Ran (Pesachim 5b in the Rif) disputes the concept of Achshavai.
The Peri Megadim takes issue with many points of the Rivash’s responsum. He notes the Gemara (Berachot 14a) which concludes that one is allowed to taste something on a fast day. But if there is a concern that one may swallow inadvertently, then it should be prohibited. The Peri Megadim attempts to answer that fast days are a Rabbinic prohibition, seemingly in agreement with the Tzemach Tzedek. But the Peri Megadim continues that accepting fast days is like a vow and may have Biblical ramifications. If so then why is tasting allowed?
 There would be no problem when it comes to the allowance of tasting on a fast day, because eating on a fast day is not based on benefit of the throat, but removing hunger in the stomach.