Snakes seems like the carnivore least likely to get food stuck in their teeth. Their whole system is set up to avoid this, actually. They only have 2 teeth, they eat their food whole, and they eat once a week. Which is for the best, really, because if a snake did get food stuck in its teeth, it would be there for a really long time. And would no doubt be seriously embarrassing. Having a vole, or part of a vole, stuck in between your front (and only) two teeth would be impossible to stop looking at once the snake opened its mouth. It is the snake equivalent of wetting your pants. It indicates that you are incapable of successfully performing a fundamental bodily function. This is no doubt why snakes carry little mirrors.
For whales, by contrast, getting food stuck in your teeth is synonymous with eating. A blue whale eats tens of millions of krill a day, catching them in its baleen “teeth.” Having krill in your teeth is probably a social sign of fitness among blue whales. At business meetings the power-player whale types hit up the bathroom to stick krill in their baleen beforehand (a trick they learned from Monster.com). This shows that they know where the food is at and, by inference, will nail this advertising campaign pitch.