Looking on the troubleshooting section of the Ubuntu wiki, towards the bottom of the page, it mentions the commands required to start Tomboy with debug messages. As follows below:
Getting debug info
One thing to note: to quit Tomboy, I had to right-click on the Tomboy icon on the panel and select "remove from panel". Check in the System Monitor (System -> Administration -> System Monitor) that the tomboy process is no longer running.
When I ran the above command, tried to sync (unsuccessfully) and checked the log file, it came up with an error of:
[ERROR 19:51:49.776] Synchronization failed with the following exception: String was not recognized as a valid DateTime.
at System.DateTime.Parse (System.String s, IFormatProvider provider, DateTimeStyles styles) [0x00000] in
Doing a search on this message revealed a couple of other people who had the same issue. One such user was here, and one of the answers pointed to this bug report here.
The solution required for me wasn't quite as drastic as what they tried - backing up all notes, deleting them from the Ubuntu One web interface and locally on the machine, syncing, then re-creating all notes. I just deleted the one note I edited from the web interface and on my local machine, and sync worked again. I recreated the note, tried re-syncing, and it all worked fine.
The moral to the story is, don't use the web interface to edit your notes. It could cause problems.