Hammurabi's final conquests are almost perfunctory, but his responses to the subsequent rebellions is anything but. Much of the episode however is concerned with the practice of religion in old Babylon and how it intertwined with everything from the daily lives of commoners to matters of state policy. Where did the superstitions of divination come from, what did they look like, and how did the average Babylonian understand his own religion?
I want to note that this episode deals pretty heavily with the practice of Sumerian religion in Babylonian times, and there are lots and lots of details that I am skimming over and simplifying. That said, this is not a dead religion, it is currently undergoing a bit of a revival, and I am doing my best to be respectful of the modern worshippers. If you are interested in the practice of Sumerian neo-paganism, I would suggest reddit.com/r/sumer for a very helpful community, or gatewaystobabylon.com for what may be the most well researched and informative source of practice and wisdom for a modern practitioner.
There is apparently a theory that Zimri-Lim actually died of natural causes and with his death Hammurabi walked into kingship in Mari with very little resistance- presumably there was no valid heir. This theory seems to me extremely unlikely, but it is one of those things where we can't disprove it, just mostly ignore it but keep it in mind should later evidence be unearthed to support it.
Additionally, the flooding of Eshnunna could by some accounts have occurred during the conquest of the city. This is a respectable, though minority opinion, and I prefer the narrative presented in the episode. Still, the possiblity exists that we could find evidence of either two floods or a much earlier date for the city flood.