First of all, most of dvd players don't support multisession if you are burning dvd movies. Come to think of it, I don't think you can even burn multisession dvd movie disk.
If you are backing up your data, you need to check that your reader reads multisession dvd disks. My dvd-rom on IBM T40 doesn't accept multisession disks, will only ready the lastest session.But all my other readers works fine. One more thing, I think only XP can handle multisession dvd (i'm not 100% sure about this)