In conversation it occasionally becomes apparent that what is coming out of your partner’s mouth is not nearly as captivating as what is not.

Everyone is familiar with this scenario: you are talking with someone and come to notice a small piece of food in their teeth.  For our purposes, let’s say it’s a potential client and a sliver of something green.  Blaspheming internally is utterly condoned by God because, put simply, there is no way out.  This is a true test of etiquette wherein the potential for blunder is great but the necessity for action is absolute.

Ignoring the offending morsel presents the very real possibility that the person will discover it on their own and be forced to wonder why you did not tell them. Secondly, it takes far too much effort NOT to say something. While they chat about price points and market share, that little piece of spinach will take on fantastic proportions and chances are that when they ask you to weigh in, your mind will be preoccupied with a newly developed fear that Popeye will come storming in at any moment and pluck the green gob from its niche.  Clearly it is in everyone’s interest to take action.
In a one-on-one scenario the solution is easy: simply wait for a break in the conversation and quietly inform the person that they have something in their teeth.  Unfortunately, life is rarely so simple so you will need some degree of discretion in implementing the plan.

The first consideration is your proximity to the person.  If you are at a distance that would require you to project your voice then you should move closer.  From more than a couple of feet, even good manners and artful wording will sound something like, “Hey sister, you gotta wad of sumthin’ in your gob!”
Furthermore, try to be specific without being overly so.  Etiquette is not a method of passive aggression so please, do not try to tell them wordlessly by fixating on their open mouth and bulging your eyes suggestively.  Use words and, if necessary, gesture to the spot on your own mouth without baring your teeth like an ape.  Since you will have some time to consider the situation before acting, figure out which side is their left before saying so. This will prevent you from wiping your faces at one another in an infinite loop of reciprocating wipes.
If the person appears embarrassed you can usually smooth things over by offering up your own anecdote of a similar situation.  This will give them time to remedy the situation while you let them know that you understand their predicament. Remember that there are no hard and fast rules here.  Your role in the spinach debacle is not unlike that of a General, you didn’t create the war but it’s up to you to make sure you’re greeted not as an oppressor but a liberator.