This seem weird to me:
dusf@banshee:~$ mount | grep BT
/media/DUMP/dusf/Downloads/.transmission/BT5R2-KDE-32/BT5R2-KDE-32.iso on /media/BT5R2 type iso9660 (ro)
dusf@banshee:~$ mkdir /mnt/sdf1
mkdir: cannot create directory `/mnt/sdf1': File exists
dusf@banshee:~$ mount /dev/sdf1 /mnt/sdf1
mount: only root can do that
dusf@banshee:~$ sudo mount /dev/sdf1 /mnt/sdf1
dusf@banshee:~$ cd cd /mnt/sdf1
bash: cd: cd: No such file or directory
dusf@banshee:~$ cd /mnt/sdf1
dusf@banshee:/mnt/sdf1$ sudo rsync -r /media/BT5R2/* .
Why did /mnt/sdf1 already exist when you tried to create it? Did you try ls'ing it before you used it as a mount point? Did you try this process multiple times?

Before trying your rsync it might be a good move to do a "df -h" to ensure you have the expected amount of free space.