Lots of interesting material in these pages; I have noted a few items here. As always, best to have a gemara in front of you for this.
The gemara connects one who eats bread without first washing נטילת ידים with one who lives with a זונה – a rather remarkable comparison! The Maharsha explains that they are related in that both result in poverty.
See Tosafot נעקר.
The gemara here translates the biblical term יקרה as “valued.” This is reminiscent of Sanhedrin 38b, in which the use of the word יקר is brought as proof that Adam haRishon spoke Aramaic; it seems that this word means slightly different things in Hebrew and Aramaic – valued vs. heavy. Of course, the two meanings are related, directly as well as in slang.
Rava says that learning Torah will not save a person from Gehennom if he sins. See the mishnah later on 20a about learning Torah to delay – but not eliminate - the effect of the Sotah water.
See Tosafot כל, who is bothered by the fact that the mishnah in Perek Chelek in Sanhedrin, which lists those who do not merit olam haba, doesn’t include the arrogant person mentioned here.
The gemara recommends an eighth of an eighth of arrogance. The Vilna Gaon famously pointed out that the eighth pasuk in the eighth parshah in the Torah begins with קטנתי מכל החסדים, Yaakov’s humble declaration that he does not deserve all that HaShem has done for him.
I also wonder about the eighth of an eighth being 1/64 – marginally less than 1/60, the shiur for nullification in a mixture… (for a similar idea, see the gemara in berachos about dreams having 1/60 of prophecy, and of Shabbos being 1/60 of olam haba, etc.)
The gemara says that one who evaluates his path, calculating his actions, will merit great things. But what if he were to calculate and decide that it would be better for him not to do a mitzvah? The same question may be asked of Pirkei Avot 2:1, which encourages calculating a cost/benefit analysis of mitzvot and aveirot!
Some of the commentaries to Avot 2:1 don’t take it as a literal recommendation; further, the game is fixed, since the reward for mitzvot and for avoiding aveirot is always supposed to be greater than any earthly benefit. For another view, though, see Terumat haDeshen 5 regarding a man who elected to skip minyan in order to claim a debt owed to him. Terumat haDeshen justifies the calculation (although he disagrees with its conclusion).