King Solomon unsuccessfully attempting to trick the Angel of Death by sending two servants who he heard were to die, to a far away place, via sheidim-Spirits - where the Angel had been supposed to kill those two servants: Succah 53a
A Divine Voice confirming Solomon's decision as to who was the mother of a disputed child brought before his court: Makkot 23b
King Solomon established the transmission of Torah, and established the signs (mnemonics?) for it: Eruvin 21b
King Solomon's enactments made the Torah, which had been like a handle-less basket, into a basket with handles: Eruvin 21b
Why King Solomon was anointed, given that he was already the heir to the throne - the concern for Adoniyahu's coup: Keritot 5b
King Solomon as "Kohelet [Ecclesiastes]"
Whether the scroll of Kohelet represents something which is divinely inspired, or is the wisdom of Shelomo: Megillah 7a
Kohelet wanted to acquire the 49 levels of understanding which Moshe had acquired; a Divine Voice informed him of the impossibility involved: Rosh HaShanah 21b
Kohelet wanted to attain the wisdom to be able to judge cases without witnesses or prior warnings to the defendants, but a Divine Voice informed him that he couldn't: Rosh HaShanah 21b
