There are other threads dealing with some of the issues. When I use Cortana in my car, unfortunately she has to deal through the deplorable Ford Sync system which creates a lot of issues. First, in order to work, Cortana has to, in effect, make a call to the Sync system so the normal, almost instantaneous response from Cortana, there is a delay of several seconds before Cortana is actually listening to me.
And the other issues are the Sync mic is awful, muffled and very low volume. And if you are making telephone calls through your car's Sync bluetooth, or listening to music or podcasts, and you have a Sync/Cortana interaction, you sometimes lose the bluetooth connection. Some of this is not specific to Cortana, and arises out of the way WP bluetooth works. I often have to turn the volume up when bluetooth has been activated, as it seems to default to a very low volume setting. You miss calls and don't realize a podcast is actually playing through bluetooth because it is so low.