At our organization, it's very common to work on multiple projects a day, for minutes at a time. It would help to have the option to track time in minutes to get an exact figure of how much time is being spent on each project or task.
How about the ability to switch time reporting on areas where time can be reported (on the time sheet, log hours function, and all other hour reporting areas) to toggle between hours and minutes. You'll probably want to look into how your reports can report the minutes as well (not sure if there's a way to do that now).
My current workaround to report in minutes is to simply keep a sheet handy which displays the values