Trello wound up being a fantastic organizing tool: items are laid out in a clear, visual manner, instead of being scattered across multiple emails. This alone is worth the price of admission, and it provides a clear demonstration of just how much superfluous verbal "glue" is required in routine communication, and how much time can be saved by efficiently cutting to the matters at end.
On a related note, it is easy to tell at a glance if something has been done, or still needs doing. This is absolutely invaluable when undertaking large, complex tasks.
One aspect was problematic, however, and it mattered to a much greater extent than I might have suspected in advance. Because this is a virtual "post-it" environment, accurate and timely notifications are critical. In each of my tests of this system, I learned that people will only use it productively if the notifications are pushed to them (i.e., if they have to take the initiative to check back in, it doesn't happen).
I, along with several other users, experienced substandard and unreliable notifications. It is entirely possible that there are some settings (beyond the obvious ones) that need to be adjusted, but part of the required utility of the system is that it is up and running quickly.
These notification problems were at the core of the students' critical assessment of the system. During times of unreliable notifications, we would revert to emails, given us the worst of both worlds: the relatively cumbersome and highly diffuse communication of email, along with potentially confusing duplication of information in another location.
However, even with these issues, the experiment was extremely productive. In a very short period of time, I saw faculty/student communication become highly efficient and focused; it became simple to track problems that needed to be resolved. It was also highly satisfying for all concerned to move issues from the "to do" list to the "done" list!
Going into the future, I plan to iron out the kinks with the notifications, but once that aspect is carefully resolved, I am very excited to use this tool in the majority of my classes, graduate advising, and staff supervision situations.