This is a good question. Even though the odor is not deemed as "bad," it is still an odor that is new or different and should be looked into.
Food smells that remain after a meal mean that food is being retained in the mouth - in vacant 'pockets' of diseased tissue (eg tumor) or from spaces created after loss of a tooth.
The drooling may indicate pain, lack of sensation, reduced muscle control, excessive saliva production, obstruction or a combination of factors.
The first step would be a look inside the cat's mouth. Your veterinarian will be examining not only the teeth and gums, but also the back of the mouth, under the tongue, and the hard palate (roof) of the mouth. The exam will also include palpation of the head and neck, checking the size of the salivary glands and lymph nodes to rule out underlying infection or disease.
Related: Bad Breath and Drooling
Problems of this type are more commonly seen in senior pets, but not always. Retained baby teeth may collect food, hair and bad odors.
Sometimes nothing is wrong. My healthy Greyhound Argos has a food-collecting area in his left cheek/lower jaw area that is not diseased, but he apparently chews more on this side. I realized this was happening by doing daily tooth brushing. Now the tooth brushing session involves a gentle wipe of the gum area to remove any remaining food.
Bad or "not normal" odors and drooling are definitely reasons to visit the vet and explore possible underlying causes to begin any necessary treatment(s).
