I've been playing around, and in my current game the AI only just got culture, so I'm able to play around with what will, hopefully, be something close to the "final" result of culture (because the AI hasn't had time to get its culture set in stone, planets don't auto-flip). There are a few UI level suggestions that came out of this:

One is some indicator of how deep a planet is in another's culture (and how long it would take to flip if colonized). Another is an indicator on my own planet on how long its going to take to flip. Also, change the constant flip warnings to something more descriptive -- I don't need to be spammed with "We've lost contact with a planet!" instead of something more descriptive of the fact that the planet is in the process of flipping. And on the planets tooltip, change it from "will flip soon" to something also more useful to the player... I don't need to be spammed with that for 3 minutes straight