What first? I'm going to go with the camera and animations. I'd really like to see the conversation view moved away from the person's face. How many of you regularly have conversations standing a foot apart from your friends? (or total strangers?) I propose this: when the player activates an NPC to start a conversation the player is frozen in place, and the camera locks to the NPC, it does not, however, zoom in. The NPC is free to move about and perform animations, but the player is centered on them. This will allow the use of full body language, fully animated reactions to dialogue, and let the NPC move about the area if the devs want them to, e.g. to show the player a map on the wall or some such.
For conversation style I'll just say I'd like something a bit more...uh...conversation like. Morrowind and Oblivion's conversations consist almost entirely of the player asking questions (which don't actually have dialogue, just terms to inquire about) and NPCs answering them. The system employed in the new Fallout games is nice, but requires quite specific dialogue for the number of NPCs that will likely be present in Skyrim. Options along the lines of "Ask about services in Solitude." or "Accuse in murder of Eydis." or "Offer to help with missing armor." Something simplistic, but more descriptive than a single word.
Finally, the the Speechcraft skill. I'll just say it flat out, the mini-game in Oblivion was stupid. I don't really have an idea for how it should be used beyond bringing in a Persuasion menu similar to Morrowind, but I'm sure one of you can think of something better.