Gemara

28b (Mishnah): If Ploni received wages for ruling about a (Mum of a) Bechor, one may not rely on his ruling to slaughter it;

The only exception is an expert like Ila of Yavneh. Chachamim permitted him to receive four Isarim (32 Perutos) for checking a small animal, and six Isarim for a large animal, whether he ruled that it is Tam or Ba'al Mum.

Question: Why did he receive more for a large animal?

Answer: It is more toil to check its Mum.

Question: Why is he paid for ruling that it is Tam? This does not help the owner!

Answer: If he were paid only for ruling that it is a Ba'al Mum, people would suspect that he does so even when it is really Tam, for his own profit.

Question: Now that he is paid either way, people might suspect that he forbids Ba'alei Mum (i.e. says that it is Tam) in order to profit, so the owner will bring it to him again after another Mum develops!

Answer: Chachamim enacted that he is paid only once for any one animal (even if he checks it many times before permitting it).

(Mishnah): If one was paid for any of the following Mitzvos, the Mitzvah is invalid - judging, testimony, being Mekadesh (mixing the ashes of Parah Adumah with the water) or sprinkling the water.

If a worker was idle from his job, one may pay him like a worker.

(Abaye): One may not be paid to sprinkle or to be Mekadesh. One may be paid for transporting ashes or filling up the Kli with water.

29b (Beraisa): One pays a worker the amount of compensation he would want to be idle from his job (for the time he engaged in the Mitzvah).

(Abaye): We account for the exertion of his job.

Rishonim

Rambam (Hilchos Bechoros 3:7): If Ploni received wages for ruling about a (Mum of a) Bechor, one may not rely on his ruling to slaughter unless he is a great expert and Chachamim know that there is no one like him, and they fixed a wage for him to see and inspect animals, whether it is found to be a Ba'al Mum or Tam. He is paid only once per animal, and he sees it whenever they bring it to him, so he will not come to be suspected.

Rosh (4:5): In Kesuvos 105a, we say that judges who made decrees in Yerushalayim used to receive wages from Terumas ha'Lishkah, even though they had no other job. That is because they spent the entire day on this, and they could not engage in work. They needed to receive income for this. If not, they would starve! Likewise, people brought Bechoros to Ila the entire day, so he needed to receive money for checking.

Rosh (ibid.): Abaye said that one gets paid (for judging or testifying) the amount one would want to receive to be Batel from his job. He is not paid at all for his testimony.

Tosfos (29a DH Trei): Even after it was enacted that he is paid only once for each animal, there is suspicion lest he says that it is a Ba'al Mum so he will not need to check to again (for free)! I answer that Chachamim did not obligate him to check it again, just if he did, he may not take wages for it. Also, people would not suspect lest he permit an Isur in order to avoid the toil of checking another time.

Rashi (29a DH Gasah): It is more toil to check a big animal, for he must throw the animal to the ground and tie it up.

Poskim

Shulchan Aruch (YD 312:1): If Ploni received wages for ruling about a Bechor, one may not rely on his ruling to slaughter unless he is a great expert and Chachamim know that there is no one like him, and they fixed a wage for him to see and inspect animals.

Beis Yosef (DH ha'Notel): The Tur understands that the Heter to receive like an idle worker applies also to one who inspects Mumim. The Rambam did not write this. It seems that he holds that the Heter does not apply to one who inspects Mumim.

Beis Yosef (DH uv'Mai): Rashi says that if he is paid, we do not slaughter based on him, lest he permitted it due to the wages. However, an expert like Ila, who was a Chasid, is not suspected. The Tur holds that anyone who does not receive more than Sechar Betelah (compensation for lost wages) may permit, even though Beis Din did not fix an amount for him. This is difficult. The Tur said that the Sechar Betelah must be evident, and later he says 'if he was a worker idle from his job...' He connotes that these are two different things. Seemingly, they are the same! Perhaps we give some wages even to one who has no job when we ask him to toil. Obviously, if one has a job and we make him lose wages and toil, we pay him more than we pay an idle man. The Reisha teaches that we do not give more than it is proper to give an idle man. The Seifa discusses paying a man who must cease from his work. The first law is learned from Ila. The second is learned from the Mishnah of Sechar Betelah.

Bach (2): The Tur says 'Sechar Betelah must be evident. And if he is a worker...' I.e. if he is not a worker, rather, his income is through buying and selling, or wholesaling, which does not earn a fixed amount each day, he may receive Sechar Betelah only if it is clear what he could have earned at the time he was checking. A worker may receive compensation based on the job he was Batel from, like it says in YD 177.

Beis Yosef (DH Aval): The Rambam connotes that Beis Din must fix a wage for him. If not, he may not take, even if it is less than what he normally earns.

Bach (1): Why did the Gemara say that only an expert like Ila may take wages? If he is not an expert, even if he is a Chasid who checks for free, one must bury what is slaughtered based on his ruling! It seems that he must be a greater expert than anyone in his city, like Ila in Yavneh. If Ploni takes money to check, and Almoni is as expert as he is and he does not take wages, even if (in other matters) Almoni is a smaller Chasid than Ploni, one may not slaughter based on Ploni, since Almoni is equally expert. If one is a bigger expert than everyone else, it is best to go to him, even if he takes wages and the others do not. I learned from the Rambam. He learned from my question, and from the fact that the Gemara mentioned in Yavneh. However, the Tur explains that he must be Muchzak in the city to be Kosher. The Rambam's Perush is primary. The Shulchan Aruch is like this, and we rule like this.

Bach (Kuntres Acharon): In YD 177, the Tur discusses Sechar Betelah of an idle worker (for one who toils on behalf of one who lent to him). There, even if he has no job at all, one must pay him to avoid Ribis. Also, here we discuss checking Mumim, which is not a toil, so if he had no job at all, he would not receive anything.

Drishah (1 DH v'Tzarich): In Bava Metzi'a, Tosfos (68a DH v'Nosen) and the Rosh (5:39) say that Chachamim were lenient about Avak (mid'Rabanan) Ribis. Regarding Bechor, we do not pay the full wage, lest there be suspicion that this is why he permits. This concern does not apply to a judge or witness who receives equally from both parties, since he cannot tilt the verdict or testimony to help both of them. However, if so, the Mishnah (that teaches that we pay as if he were totally idle) applies only to checking Mumim (which the previous Mishnah taught), but not to judging or testimony, which were taught in the same Mishnah. This is difficult. Rather, the Tur does not compensate for the toil of the Mitzvah if the worker normally works the entire day, for then he is happy to rest and be compensated, so he can work better later. If one works only part of the day to earn what he needs, he does not want to take less money to cease in the middle. A better answer is that if he stipulated, he receives compensation also for the toil of the Mitzvah. If not, we view him like one who ceases work and is totally idle.

Taz (1): Regarding Hashavas Aveidah, the Tur (CM 264) discusses Sechar Betelah of one who has a job. There and here and regarding Ribis, the Gemara said 'Sechar Betelah of the job he is Batel from. Tosfos in Bava Metzi'a (68a DH v'Nosen) said that said that regarding Avak Ribis, which is only mid'Rabanan, Chachamim were lenient if one pays (even a small amount,) as if he had no job. For Hashavas Aveidah, one must pay him for his loss from his job. Since the difference between the toil of his job and the toil of returning influences the compensation, he is paid for returning. Even though one may not take money for this (or other Mitzvos), since he is paid for lost wages, he may receive also this. The same applies to judging or checking Mumim. Why did the Tur say that we consider as if he is idle from his job and does nothing? He must hold that this is not a toil. Surely one may take for traveling to see the Mum, just like one may be paid for transporting ashes or filling up the Kli with water.

Note: The Gemara said that Ila received more for a large animal, for it is more toil to check its Mum. How can the Bach and Taz can say that the Tur holds that one is not paid for checking itself, since there is no toil?!

Nekudas ha'Kesef: The Drishah already asked the Taz' question. It applies also to the Rosh. Ma'adanei Melech could not resolve this. I have a better answer than the Taz. Regarding unloading, the Rosh said that if the owner is there, one who helps unload could have stipulated with him to be compensated for his toil. Since he did not, Chachamim did not enact this for him. The Tur says similarly in CM 265. Also regarding Bechor and testimony, the owner is there, so Chachamim did not enact compensation for toil. However, here the Rosh says 'he does not get paid for testimony.' This is difficult for my answer, and also for the Taz'.

Bach (2 DH Kasav): The Mishnah teaches how much Chachamim allowed Ila to take for each animal. This supports the Rambam and Shulchan Aruch, who say that Beis Din must fix an amount for him.

Shulchan Aruch (ibid.): One must pay him whether it is a Mum Kavu'a and he permits it, or whether it is not Kavu'a. He is paid only once per animal, and he sees it whenever they bring it to him, so he will not come to be suspected.

Question (Beis Yosef DH u'Mah she'Chasav Rabeinu): Why did the Tur bring in the name of the Rambam that he must be paid whether he rules that it is Tam or a Ba'al Mum? The Gemara explicitly says so!

Answer (Bach 3 and Taz 3): The Tur cited the Rambam to show that he holds like the latter answer of Tosfos, that he is obligated to see the animal again when it gets another Mum.