Worth noting: The Rosh on "tipol hanaah l'hekdesh" on the Mishnah on 33a. His approach (as opposed to that of the Ran) is remarkable.
35b mentions the issue of using a moch as a means of contraception, and seems to permit it in certain cases in order to prevent danger to the life of an infant (in the case of a nursing woman), a fetus (in the case of a pregnant woman), or a very young woman. It's worth noting that where the Rosh and the Ran here, as well as Tosfos in Yevamos, take the logical position that use of this moch is mandatory, Rashi in Yevamos disagrees and contends it is optional. This view is difficult to understand, if we are talking about protecting a life!
On 36a we mention a concept which also came up toward the end of Kesuvos, of disavowing a shaliach if the shaliach's actions work against the meshaleiach's perceived best interests. From a theoretical standpoint (and juts my own thought), there are a couple of ways to understand this disavowal: (1) The mission did not include this action (ie making the item pigul), or (2) Shlichut is inherently invalid if it harms the sender, because one cannot acquire liability for a person without his explicit consent.
Practical ramification: What if I did license that specific action, but I didn't realize it would lead to a liability? As in: I told the Kohen he could plan to eat the korban tomorrow, not realizing it had to be eaten today.
No. On second thought, I don't think that idea works - if it were correct, then according to the view that Kohanim are our shlichim, a kohen could never create pigul!In any case, Shlichut is stronger than "zachin," and doesn't depend on producing merit/gain for the sender. When I empower someone to be my shaliach, he can create liability as well as zchut for me.
The gemara on 36a also talks about challenging one's children to race to Yerushalayim, and figures into two interesting discussions - the legitimacy of Bereirah, hinted at in the Ran here and discussed more fully in Gittin 25a, and in the issue of gambling as well. I cannot recall the reference for the gemara on gambling at the moment, but I think it's a gemara in Shabbos.
37 is a hugely fun daf, with a lot to see.
Keep a close eye on the Rosh throughout, particulary his note on "Aggadot" which might prove contentious in some circles, depending on what you do with it.
On "schar shimur" go with the Rosh's graphic explanation - but note that Tosafos believes children from the age of 10 already don't need babysitting. This certainly worked for their children, who were apprenticed at vocations at a very young age, but today it is hardly the same.
Shemuel gives a piece of medical advice on this page, which is consistent with his general role as the Gemara's doctor-on-call. See my page here for some.
Re: Ran on "itur sofrim" - See Rashi Bava Metzia 60a and Tosafos Sanhedrin 60a on the Torah using certain language to sound nicer (na'eh yoteir).
Put yourself through the effort of reading the GRA's fine print on the pesukim at the bottom of 37b, top of 38a.
And, of course, the big point - women should be taught to lein, it appears. Presumably this is because it will help them learn the pesukim properly, although it has added advantages; when I leined as a teenager, my mother was the one who listened to me to correct my mistakes.