So I'm playing a random huge game, invaded an enemy system, took some planets, and started getting a foothold. The AI did not like this and fired a Kostura at a Terran planet bordering the star, where i had specced for social and constructed a bunch of media hubs to push back culture faster/ make it harder for the enemy ai to do anything. I figured it was no big deal, since they would just start spreading culture again after the disable wore off, right? At first, they didn't, which I thought was weird, but I decided to wait, figuring maybe they were and it just hadn't updated on the planet info sheet yet. However,my culture began to be pushed back from the sun, which didn't make any sense for a full social spec Terran planet with 5 culture centers in orbit, so I decided to scuttle a few of them and rebuild and see if that helped.
Coincidentally, before this decision I got hit by a second Kostura. My 2 remaining media hubs (which I had decided not to scuttle for some reason) began spreading culture again after the second disable wore off, and the planet sheet updated accordingly immediately. Just to make sure I wasn't hallucinating, I scuttled them as well, and the culture spread rate dropped. So in otherwords, it seems that Kostura warheads will sometimes, but not always mess up culture spread from a planet specced into social.
Also, population values are still weird with social spec, some of my full social spec terrans have 900 pop, some have 742 pop, and one has 1222 pop, with no apparent differences between the planets that I can see. (this is after 1.51, I know I have the patch installed correctly because my Envoys are in fact 4 pop.)