Once Cortana is searching for available times, it isn't clear whether my last instructions to it triggered some action. For example, I was asked for direction after Cortana found that some people on my attendees list were out of office. I replied stating that Cortana should schedule the meeting regardless, however, that action was never registered. It would be useful to get some UX feedback from the scheduler about what state it is currently in so that the user can have a better understanding of what is needed.

When asking Cortana to reschedule an existing meeting, she does send out new meeting proposals, however she does not cancel the original meeting invite (until a new time has been found).
When the request to reschedule comes shortly after the original invite, this leads to participants still accepting the original invitation, and therefore ignoring the request where Cortana proposes new times to get the meeting rescheduled.

If the original invite was any date closeby, this would lead to participants showing up for a meeting that is being rescheduled - which is a bit unprofessional ;-)

Allow us to select verbose, or limited/varied levels of "chattiness" from Cortana, to let me know she's trying to book, but an individual is not answering/responding. In some cases I would like to keep a closer eye on the booking, versus letting it happen when it happens.