I hope that as developers we're able to take advantage of this conversational style. At the moment, WP apps can hook into the rather limited "Tell Me" system that lets the user open various endpoints of an app via voice commands, and only using pre-defined parameters.
It would be awesome if the user could pass in any arbitrary data via voice commands (devs could make custom scheduler/todo list/note-taking apps that can receive data from Cortana), and even more so if voice commands could launch background tasks instead of just the entire third-party application (you could check into Foursquare without actually opening the Foursquare app and disrupting whatever you're doing).
Did you try Wit.AI?  It's cross platform and totally open: you can create any voice command you want by just providing a few examples of what you expect. Then the API turns speech (or free text) into JSON.
Since you have access to Cortana's notebook, you can set boundaries as to what she tracks about you. This and what I heard about them making Cortana work offline, I just hope Apple and Google would follow suit. Honestly, I am just tired of storing every bit of information about me in the "cloud".
If I remember correctly they did mention the Offline part when they first revealed about Cortana. I think their plan is to do offline language processing with possible online cross checks where cellular internet service is either terrible or nonexistent. So in parts of Asia where cellular internet is slow, it wouldn't appear laggy.
I seriously doubt that Microsoft has such advanced language processing capabilities that can work offline on a smartphone. For example, as of a year ago, Xbox speed recognition was still based on an ancient technology derived from Tellme networks, you can see it by yourself during Xbox One voice recognition demos. And now you're saying that phone has more processing power to do that better than a full blown gaming console?
I've been waiting for this, being able to ask siri(Cortana) to set my nest or lock unlock the Lockitron would be awesome. Even better would be an IFTTT app that could run certain scripts based on certain phrases. Like "Good Night Cortana" would adjust my thermostat, lock the doors, and turn off any lights that are still on and make sure my alarm is set.
This is a feature that would make me interested in switching to a WinPhone