Can't Get Files Off Of Old Hard Drive On New MacBook Pro
Perhaps its the way you're wording it, but it probably would have been easier to connect the laptops together in target disk mode (hold T when turning on the old macbook), assuming you have the correct cables.  It should then appear as an external drive on the new macbook.  

Anyway, Mtn Lion should read the drive without issue as 10.6 uses the same native mac filesystem as 10.7 and 10.8 (journaled hfs).  Are you able to use terminal to list files?  Perhaps it's an issue with Finder taking forever to list the directory.  I would try Disk Utility again or run fsck -fy on the volume to force a filesystem check if you know that the old drive is in good working order.