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 Summary 

An esrog that was pierced by the teeth of rats: Rav: It is not hadar [and thus possul]. 

 Challenge: But “Rabbi Chanina would dip the esrog [in oil] [and chew a piece of it] and then use the esrog”. (So we see that even an esrog pierced by teeth is kosher).

 Question: Isn’t Rabbi Chanina opposed by the mishna (28.1) which disqualifies a pierced esrog? 

 Response: The mishna can be referring to the first day of Yom Tov, while Rabbi Chanina used the esrog on the second day.

But according to Rav, since it’s disqualified by not being hadar, it should be possul on the second day as well (the arba minim are disqualified for all of yom tov only if it is possul because of ‘hadar’, see 24.5)?

 Resolution: An esrog that was pierced is kosher on the second day, but if it was pierced by rats, it’s disgusting and not hadar. 

Some say: An esrog that was pierced by the teeth of rats: Rav: It is hadar despite being chewed upon, because “Rabbi Chanina would dip the esrog [and chew a piece of it] and then use the esrog”. (So we see that even an esrog pierced by teeth is kosher). 

 Question: Isn’t Rabbi Chanina opposed by the mishna (28.1) which disqualifies a pierced esrog? 

 Response: The mishna can be referring to the first day of Yom Tov, while Rabbi Chanina used the esrog on the second day.

 We learned in the mishna (28.1): A small esrog: Rabbi Meir: It must be the size of a walnut. Rabbi Yehuda: It must be the size of an egg. 

 Rafram bar Papa: The same machlokes can be found regarding avanim mekurzalos (stones that are used as toilet paper, either ‘smooth stones’ or ‘elongated stones’. While stones may not be used on Shabbos, Chazal allowed for what is necessary for personal hygiene): 

 Beraisa: Three avanim mekurzalos may be taken* in to the restroom on Shabbos. Rabbi Meir: Stones the size of a walnut. Rabbi Yehuda: Stones the size of an egg.

We learned in the mishna (28.1): A large esrog: Rabbi Yehuda: He must be able to hold two in one hand. Rabbi Yosi: Even if he can only hold one in both hands, it’s kosher.

 Beraisa: Rabbi Yosi: Rabbi Akiva once lugged an esrog to the synagogue on his shoulder [it was so large]. Rabbi Yehuda: That is no proof, the Chachomim said to him that he cannot fulfill the mitzvah with such an esrog which is not hadar. 

Click here to listen to the shiur with Tosfos: https://drive.google.com/file/d/1o0LtEvylz1gZIZ3sBYUYUWFVh_4bIeac/view?usp=sharing 

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* According to Rashi the issue here is muktzeh, because he is carrying it less than 4 amos in a karmelis [they relieved themselves on open fields]. 

 Tosfos: The beraisa states “to take in”, additionally, the word ‘beis hakisei’ is used which does indicate a room. Tosfos explains that the permission regarding these stones was to carry them from a karmelis to a reshus hayachid. Actually handling muktzeh is more severe than carrying in a karmelis, so Rashi should admit that it is permissible if he believes muktzeh was permitted here. Nowadays when it’s possible to prepare before Shabbos, this special permission does not apply.