Q. Is it permitted to use toothpaste or teeth whitening agents that contain glycerin?
A. Horav Tzvi Tsvi Heber Shlit'a (Director, Community Kosher - COR Kashruth Council of Canada), answered: "that Colgate, Crest and Sensodyne in Canada use vegetable glycerin.
Otherwise, some are machmir, (stringent), while others permit. The leniency is based on the idea that toothpaste is a non-edible which is made for tasting and not ingesting. There is no concern that he might come to swallow it unintentionally since it is not food and not made to swallow. If this shaila is l’maaseh (actual) then its keday (worthwhile) to ask Rabbi Miller."
Horav Shlomo Miller's Shlit'a opinion is that as it seems to be from the available internet information, most glycerin available these days is from vegetable sources, one may indeed relay on this leniency as explained by Horav Heber.
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit'a.