I 've noticed that the victory conditions for KH in the advisor bubble (when you click the ? button) and on the map screen (screen that comes up when you press the button next to the end turn button) are different. Specifically, the advisor VC do not include anything east of the Greek mainland, or the Macedonian/Epeirote starting provinces.

I 've also noticed that getting command stars with KH is considerably easier compared to the Romani, Qarthadastim and Baktria (i 've only completed campaigns with these factions). I just fought an assault on a Byzantion (sieged for 1 turn, to get the rams) with Akrotatos (3-stars) and a high quality unit/exp stack, 830+ men. The enemy was a Pontian 6-star general with 2 Pantodapoi and another 2 Pantodapoi outside the city walls, 270 men. I won easily, with less than 30 casualties. Akrotatos gained 2 stars from this siege! I fought 1100+ men Gallic stacks with 14 unit Romani stacks (570) and I was lucky if I got 1 star after 3 such battles.