Having special clothes for more important occasion has a source in the Torah from the Kohen having special clothes for taking out the ash from the mizbeach thst were lower from regular בגדי כהונה.

A talmid chochom must be especially careful that they appear neat and respectful. Their shoes shouldn’t have double patches, their outer clothes shouldn’t have any stains, and the inner shirt shouldn’t have a semen stain. The reason it that it causes ppl to dislike that Torah.

When immersing tamei items, no chatzizas can exist blocking the water. A grease stain on a garment or saddlecloth can theoretically be a chatzitza, but the rule is that חציצה is into something one is particular to remove. So small little stains may not be chatzitza. There’s a dispute if a grease stain only on one side is a problem or not. Acc to one opinion it depends on what type of clothing it’s on- on Torah scholars/fancy bath attendant clothing, it’s more likely to be a chatzitza.

To be qualified as a real talmid Chachom that’s worthy of being public leader all over, one must be able to respond to questions asked from any topic.

R Yannai requested to be buried in colored clothing, not white or black, so he wouldn’t stand in the afterlife in either Gehonim or Gan Eden.

Acc to r yishmael, Shabbos has more holiness than Yom Kippur. We derive from the pasuk that leftover fasts from Shabbos offerings can be burned the next night on Yom Kippur. But leftover fats from Yom Kippur offerings (Friday) can not be burned on Shabbos. Acc to r akiva Shabbos and Yom Kippur are equal and no fats from can be burned on other days. However, a regular Yom tov is certainly not as holy as Shabbos so leftover fats from Shabbos May be burned on Yom tov.

On regular Friday, there were Shofar blasts blown before Shabbos to inform ppl to stop doing melocho. If Yom Kippur was Friday they didn’t blow. (Even though acc to r yishmael it could be informative for the future that Yom Kippurs sanctity is less than Shabbos and fats from Shabbos could be burned on Sunday Yom Kippur, they didn’t blow for this, bc kohanim know all this well and are זריזים).

On Shabbos, there is a rabbinic prohibition against trimming vegetables and readying them for chopping. It’s excessive labor on Shabbos. On Yom Kippur, it is allowed in the late afternoon bc it brings more pain to the one fasting which is a good thing (rashi) and brings out more עינוי. This is one exception of melocho pemitted on Yom Kippur that is forbidden on Shabbos. We don’t blow the Shofar to educate about this heter bc our focus on bowing Shofar is to instruct what is forbidden and not to instruct what is permitted.