Include a button to make "events" appear differently to tasks to differentiate what can move/roll over and what can't
When adding an appointment or "event" that has a definite set time, would be good to differentiate these from tasks to which you want to assign a start time just to help you focus or to plan the day. It would then be clear which tasks can roll over and which are fixed. If they appeared in a different colour it would also be useful to flag up appointments/meetings etc. - I find that they sometimes get lost in the list of small work tasks for that day.