I am able to install media_mover-6.x-1.x-dev (dated 22 March 2012) by first installing 1.0-beta9, and then upgrading to 1.x-dev.
However, if I try to install 1.x-dev without first installing 1.0-beta9, then I get this error when I try to enable the media_mover_api module:

user warning: You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'fid (cid, fid), INDEX cid (cid), INDEX harvest_file (harvest_file), INDEX pro' at line 16 query: CREATE TABLE media_mover_files ( `mmfid` INT auto_increment DEFAULT NULL, `nid` INT unsigned DEFAULT NULL, `fid` INT unsigned DEFAULT NULL, `cid` INT unsigned DEFAULT NULL, `harvest_file` VARCHAR(255) DEFAULT '', `process_file` VARCHAR(255) DEFAULT '', `storage_file` VARCHAR(255) DEFAULT '', `complete_file` VARCHAR(225) DEFAULT '', `status` INT unsigned DEFAULT NULL, `date` INT unsigned DEFAULT NULL, `data` MEDIUMTEXT DEFAULT NULL, PRIMARY KEY (mmfid), INDEX mmfid (mmfid), INDEX nid (nid), INDEX cid,fid (cid, fid), INDEX cid (cid), INDEX harvest_file (harvest_file), INDEX process_file (process_file) ) /*!40100 DEFAULT CHARACTER SET utf8 */ in /mysite/includes/database.inc on line 551.

Also, fyi, when you install 6.x-1.x-dev, the version listed in the .info file and displayed on the modules page is 6.x-1.0-beta7+24-dev