http://revach.net/article.php?id=3922

Section: Halacha   Category: Shabbos
Rav Shlomo Zalman Auerbach & The Minchas Yitzchok - Are You Carrying Food Between Your Teeth?
All the poskim agree that going out to a Reshus HaRabim on Shabbos with food in your mouth is considered carrying.  What is the halacha if you have food stuck between your teeth, is that also considered carrying?  Must you clean your mouth well before going out?

The Shmiras Shabbos KiHilchoso (18:2:8) brings from the Minchas Yitzchok that whenever possible you should take out food stuck between your teeth before going out, since this is  completely normal and not any sort of Shinui.  He compares it to phlegm in your mouth which is assur to walk with in Reshus HaRabim once it has become detached and entered the mouth cavity.  He also brings from the Minchas Shabbos holds that this is not a normal way to carry however it is best to be careful not to do it anyway.

Lastly he brings from Rav Shlomo Zalman Auerbach who holds that you need not be machmir even in a real Reshus HaRabim, unless the food is sticking out from between your teeth and it looks disgusting or it really irritates you.  Only then would it be halachicly similar to phlegm which will be spit out eventually and is therefore considered carrying.

Important Note: We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. One should learn the tshuva to verify the accuracy of our interpretation.  Please also understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.