The Mechaber (444:4) says you should shake out the crumbs from the tablecloth after everyone is finished eating the chometz on Shabbos Erev Pesach. The small crumbs do not have to be brought out of the house since they will become destroyed by people walking on them. In earlier times when there were dirt floors it was prohibited to sweep since one was leveling out the ground. In our times, however, it is permitted to sweep and one should do so after finishing eating the chometz.
The crumbs should be flushed down the toilet. The broom should be cleaned out by shaking the crumbs either into the toilet or into a public domain if there is an eiruv. One should also pour ammonia or the like on the broom. In general, it is prohibited to wash the floor. However, Reb Shlomo Zalman zt”l says that if there is an area on the floor which is very dirty, one may pour water there and dry it with a shmata that he won’t need to use, taking extreme care not to do sechita.
How should one clean out his mouth on Shabbos after he finishes eating the chometz? Reb Nissim Karelitz zt”l says that one may use a dry toothbrush, unless he knows for sure that his gums will bleed by doing so. He may wet his mouth first. One should try to use a soft toothbrush that does not cause bleeding. Afterwards one may rinse out the toothbrush from any chometz that may be there. It is prohibited to use toothpaste. If one can use a toothpick in between his teeth without causing his gums to bleed it is best to do so.
To clean dentures, one should brush them with a dry toothbrush after pouring a little water onto them. He should then dry them off well and pour hot water onto them from a kli rishon. Many Poskim hold that this should be done on Erev Shabbos, and one should not eat any hot chometz afterwards. The same applies if one has fillings or crowns from metal, they should be careful not to eat any hot chometz on Shabbos.1
Prepared by R’ Avrohom Yehoshua Ziskind
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1Sources: Dirshu, Piskei Teshuvos