Juan,
My standard backup technique is to use mysqldump to create a backup of the
database.
I have often used this to move Moodle to different servers for testing purposes and I also keep a backup
server running and use the sql file produced by mysqldump to update this.
This has always worked fine for me, even when I have used a newer version of moodle on the target system to the one that the file was dumped from. In this instance moodle just treats this as a standard upgrade and makes the appropriate changes to the database automatically.
I think your problem may lay elsewhere than the mysqldump, though I agree with Pedro, that you should check the switches used with mysqladmin to ensure that it backs up correctly.