I'm having the same problem using the 5.1.1 dvd Knoppix distro and an 8gig Corsair VoyagerGT flash drive.
so far I have managed to changed ro mode to rw for my flash drive (sdb4 on my sys) as well as for the two partitions of my hard drive (sda2 and sda5), but only for and through the root.

when I type mount in root I get (this is from memory, as I haven't had the time to setup the network for it yet):
/dev/sda2 on /cdrom ntfs (ro,.... can't remember the rest)
/dev/sda5 on /cdrom ntfs (ro,.... same)
/dev/sdb4 on /cdrom none none (rw, open)
then there are the two cloops
and then the ###knoppix added
/media/sdb4 on /cdrom vfat (rw, ....,umask=000,... again can't recall the rest)
/cdrom on /media/sdb4 and same as above.

that's after I already did:
mount -o remount,rw /media/sdb4
mount --bind /cdrom /media/sdb4

At this point I can write to any of the drives from the root shell (including /cdrom), and only from there.

It's impossible to mount anything from the desktop, whenever I try it opens up the /cdrom dir

My guess would go toward the binding to the two sda partitions (my hdd with xp and storage partitions), but it's just a guess, as I'm still quite a newbie with Linux in general.

Oh, and my flash drive is formatted into one bootable partition (7.7GB), and boots in about 15 seconds, which is beautiful, but with out any form of rw, even to other drives, it kind of defeats the purpose.