|To see this picture debunked, see here|
On Shabbat daf 12: Lice and teaching a trade -- Did these Amoraim drown the lice on Shabbat or chol? Perhaps the parallel Yerushalmi can help disambiguate. And in terms of the permitted activities on Shabbat:
One must not negotiate for the betrothal of children [girls],23 nor for a boy, to teach him the book24 and to teach him a tradeWe know the associated Shabbos zemer, but what to make of lamnatzeach binginot?
On Shabbat daf 13: Why Ulla kissed his sisters' bosoms -- explaining how bosoms and hands might have switched off, girsologically speaking. And how Ulla does not necessarily hold 'Take a circuitous route, O nazirite, but do not approach the vineyard' applies to closeness to forbidden relations.
On Shabbat daf 14: When was the first gezeira enacted --I suggest that Tosafot's question is actually a rather strong question.
On Shabbat daf 17-18: Trying to get to the bottom of the dispute between Beit Shammai and Beit Hillel about starting a melacha which will finish on Shabbat.