Eject disk and get error message "Disk not ejected properly" when unplugging disk
I think I found the issue. There was some minor damage that the disk had. Disk Utility was able to fix the problem, and the dialog box no longer comes up when I unmount the disk and then unplug it.

I'm still trying to understand how this would cause the error message. It took over 40 minutes for Disk Utility to scan the disk before this problem showed up on the Disk Utility log. The error was Invalid leaf record count (It should be 23755134 instead of 23755132).

As I stated before, the Console doesn't show this issue. In fact, looking at the mount and unmount on /log/fsck_hfs.log, I see this entry:

/dev/rdisk2: fsck_hfs run at Wed Mar  6 18:35:07 2013
/dev/rdisk2: ** /dev/rdisk2 (NO WRITE)
/dev/rdisk2:    Executing fsck_hfs (version diskdev_cmds-557~393).
QUICKCHECK ONLY; FILESYSTEM CLEAN


which pretty much means a quick check on mount finds no errors. I have no idea how this would cause the error dialog box to show up when I unmount the disk successfully, and then unplug it.