There is a ton here on these pages; see Rashi and Maharsha on pretty much everything.
In my notes here, see especially the note on how we respond to suffering, the significance of clothing color, and the stories of Reuven and Yehudah. As always, having a gemara with you will help.
Abayye is seen responding to Rava here, which is unusual. In general our edition rejects having Abayye, the mentor, question Rava, the student, and Rava’s name רבא is consequently changed frequently to Rabbah רבה – since Rabbah was Abayye’s mentor.
See Tosafot אם; this is an important point regarding the way we handle problems in life. Rather than observe idiosyncratic situations and ask ourselves why they are happening, we tend to explain away idiosyncrasies with pat answers, ignoring warning signals.
It’s odd, to me, that we would destroy a valid korban due to a rabbinic concern. I recall that in Zevachim we specifically say not to do that?
The word כפרה (kapparah) is not specific to atonement for sin; Rashi notes that here, on the gemara’s use of כיפרה.
Rashi’s version of a technical התראה warning, in "דידעי", does not fit the normal format of התראה.
In the first mishnah: If they are going to Yerushalayim anyway, why does the local court get involved at all? Just to provide escorts?! Perhaps this is why the Rambam writes (Hilchot Sotah 3:1 – note that this is mislabeled in the עין משפט on the daf) that the local hears and evaluates the testimony before sending them on.
The black clothing as a sign of mourning is interesting; see Pesachim 109a on colored clothing being joyous, and see Shabbos 114a especially, and see Yoma 19a (Kohanim ineligible for wearing black), Bava Metzia 59b (black for a solemn, sad occasion), Moed Katan 17a (black clothes for the person who wants to sin), and Maharsha to Sotah 22b (black clothes as a sign of mourning), Maharsha to Kiddushin 40a (black clothes against the yetzer hara), and more. Of course, also see Yeshayah 1:18 and Kohelet 9:8 on white and innocence and joy, and Shulchan Orach Chaim 610:4 on white clothing for Yom Kippur.
See the Rambam on the mishnah regarding לבה גס בה – the concern is that being with familiar people bucks up one’s spirit.
What was Yehudah’s sin? Being with a zonah was permitted, and punishing Tamar for apparent extramarital involvement (because the גאולה bond to Shelah and his family was quasi-marital) was legitimate! Note that Rashi and Ibn Ezra to Bereishit 38 both say the embarrassment for Yehudah actually came from giving over such expensive and personal items for the sake of a liaison.
How could we tell her Reuven sinned, of the gemara in Shabbos says explicitly that Reuven did not sin? Rashi here seems to say it’s just moving the bed that is the sin. Rama (in his Responsum 11) has a different view, though – he says we lie about Reuven, giving him a bad reputation, for the sake of restroing shalom in general and avoiding erasing Gd’s Name.
See Rashi on להם לבדם נתנה הארץ.
See Rashi vs Tosafot on לא עבר זר
The idea of reward for Teshuvah fits nicely with the gemara in Yoma on proper teshuvah converting sins to זכויות, merits.
Rashi gives you the very interesting backstory on why Yehudah’s bones rolled in his casket.
The gemara’s idea of the person feeling posthumous pain when his body is harmed is reminiscent of the big discussion in Berachot 18b on whether a person experiences pain while the body deteriorates.