"It's About Time", more than any other episode, convinced me that there really needn't be a major change in the show's dynamic with Twilight becoming a Princess. All she's really missing in that one is the title, after all. She takes it upon herself to mobilize all of Ponyville to prepare for a disaster based on her word alone, and no one challenges her authority in the least. In fact, it reaches well beyond Ponyville, as Rainbow Dash reports that she has Pegasi reporting in coast-to-coast across Equestria, all on the say of a Librarian.
Of course, that Librarian happens to be the Princess's personal protégé, one who was specifically sent "to supervise Ponyville" by the ruler of the land in the first place ahead of the Summer Sun Celebration. She was introduced to all of her friends as the representative of the crown who had final say in approving all of their hard work, and that authority over them didn't seem to be a barrier to forming world-saving friendship with her anyway. So really, I can't see the Princess thing really getting between them now.
What's interesting to me is the way that Twilight has wielded that power she has over the course of the show. When something needs done she seems to have no qualms about simply giving orders, whether it's telling her friends what to do in a crisis, or calling to disaster-proof all of Equestria or simply telling ponies to repaint a banner welcoming Celestia. And ponies seem to expect that of her... when too many Pinkies overrun the town, the mob gathers outside the library, not town hall, to demand action, obviously seeing her as the go-to for situations like this. Perhaps most interesting, however, is that she doesn't seem to notice that she wields that kind of influence... When the time came to break into the Starswirl the Bearded wing, Twilight was the only one who questioned her authority to be there. Despite it being guarded and locked, the guards and Celestia herself didn't bat an eye at her having access without asking.
Adding the "Princess" title seems like it's going to bring a bit of extra ceremony to things (and finally make her recognizable to the upper crust of pony society), but otherwise I doubt it'll change much, personally.