Where’s the free space gone on the MP3 player

You will not be able to reclaim this space to your OS X partition unfortunately. That is because the Recovery HD partition is in between your OS X and (formerly) Ubuntu partitions. You have two options:

• In the partitions tab, click the "+" and add a new partition. OS X will see this new partition as a separate drive, but it should be fully useable. However, it certainly complicates things vs. having a nice big single drive to work with.

• Backup your Macintosh HD and wipe the entire hard drive (booting from another volume, such as Internet Recovery or Gparted on a disc). Then reinstall OS X, allowing it to properly recreate your partitions. This is more cumbersome but recommended.

When I partitioned my Mac for Ubuntu (using rEFIt) a while back, I ended up doing the second option to make my Mac "normal" again.

I know you "don't want to reinstall OS X," but the easiest way to reinstall Quicktime (the current version, which is not a standalone download) is to reinstall Mountain Lion via Recovery Mode. Following the introduction of Lion, Quicktime became apart of the OS X installation package. There is no need to take a roundabout method. Reinstallation using recovery is non-destructive and only reinstalls OS X builtin applications and system components.