Kiddushin, Chapter 4, Mishnah 5. In the previous mishnah we learned that when a rumor of invalid lineage has gone out about a family, a kohen who wishes to marry into it must investigate eight ancestors on the father's side. Our mishnah comes to set the limit of that investigation: "Ein bodkin lo min hamizbe'ach ulema'alah" - there are certain points at which, once the investigator reaches them, there is no need to continue checking the generations that preceded them.
Three points at which the investigation stops:
"Ein bodkin lo min hamizbe'ach ulema'alah" - if somewhere in the chain of ancestors there is someone who served as a kohen in the Beis HaMikdash upon the altar, there is no need to check beyond him. (Bear in mind that the count of eight was stated regarding a kohen, while for the daughter of a Levi or the daughter of a Yisrael the count is larger.)
"Velo min haduchan ulema'alah" - the same applies to the daughter of a Levi: if one of the ancestors served as a Levi in the Beis HaMikdash and stood and sang on the duchan, the raised platform, there is no need to check into his mother or into any of those who preceded him, since such men were already investigated before they were permitted to serve.
"Velo min haSanhedrin ulema'alah" - the same is true if one of the ancestors served in the Sanhedrin, for we know that all the men connected with the Sanhedrin were of established lineage, and there was no flaw of lineage among them.
Public officers and charity collectors:
The mishnah adds: "Vechol shehuchzeku avosav mishotrei harabim" - one whose ancestors are known to have been among the officers, those who enforced the law on behalf of the beis din, and likewise appointed charity collectors. The Gemara explains that this refers specifically to Jerusalem, whose officers were appointed only if they came from a family of established lineage. All of these "masi'in lakehunah ve'ein tzarich livdok achareihen" - they may marry off their daughters or their granddaughters to kohanim, and once the investigator has reached such an ancestor, he need not investigate any further.
Regarding the charity collectors, the Gemara explains that the reason is not specifically that a man would not be appointed without checking his lineage and his family chain. The reason is different: in those times a fixed amount of charity was set that was required of every person in the community, and the collectors would take a security deposit for the charity, something that caused people discomfort and anger. Therefore, had there been any flaws in the collector's lineage, that would have served as ammunition against him in the hands of those from whom the security was demanded. It follows that if no problems arose, we may assume that any invalidity would already have come to light.
Testimony in beis din and enrollment in the king's army:
Rabbi Yose says: anyone who signed as a witness in the beis din in the old city near Tzippori - he too is included among those of established lineage and may marry into the kehunah, since a man whose lineage was not clearly established would not have been allowed to sign as a witness.
Those enrolled in the king's armies: anyone who was registered among the king's soldiers. The Gemara explains that this refers to the armies of King David during his reign, and therefore it has no practical application except in ancient times. The reason: they would not include among those soldiers anyone whose lineage was not clear, because they wanted the merit of their fathers to stand by them and assist them in battle.
In summary: our mishnah establishes the limits of the investigation into lineage - the altar, the duchan and the Sanhedrin - upon reaching which the investigator need not continue checking the generations that came before. Also listed are those whose ancestors were among the public officers or the charity collectors, those who signed as witnesses in the beis din of Yeshanah, and those enrolled in the armies of the House of David: all of them may marry into the kehunah, and there is no need to investigate them further.