Filesystems mounted on the filesystem you're trying to unmount can cause the target is busy error in addition to any files that are in use. (For example when you mount -o bind /dev /mnt/yourmount/dev in order to use chroot there.)
To find which file systems are mounted on the filesystem run the following:
mount | grep '/mnt/yourmount'
To find which files are in use the advice already suggested by others here:
lsof | grep '/mnt/yourmount'
