I've gotten pretty good at the game to this point, and am playing Vasari at the moment (great race in this game with a solid distinct style).
I usually get to the end of the game with 1 opponent remaining, and go to war with him, usually after being at peace and destroying the second to the last civilization. Prior to wiping that last civilization, I make a point to put major fleet elements in the last empire's homeworld, to smash his frigate/cap factories and engage fleets as they come in piecemeal.
But here's where I get my butt kicked. I start loosing worlds all over the board to cultural attacks, with my loyalty dropping to zero percent. Not sure of how this happens or what to do to defend against it. I'm playing against TEC, and have lost around 6 worlds to this type of attack whilst smashing the opponent's homeworld and his fleets. My counter is to build propaganda facilities (forget hte name, but they expand your civ's culture to neighboring planets), and try to destroy his nearby broadcasting centers and such. I usually win the game against the AI either on normal or difficult, but this is my achilles heel.
Any tips?