Q: Is there a way to clean up the disc on my Apple Mini?  Similar to, say, the "scan disc" or "clean disc" features on PCs that helps to clean poor files and organize files to make best use of disc space.

The software for this is Mac OS X, it runs every second your Mac is turned on maintaining your Mac, you don't need any additional tools.

Delete the work files you no longer need and keep the rest.

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Try:

Troubleshooting wireless mouse and keyboard issues

Also when yo are having problems run this and copy and paste the results here:

EtreCheck

ScanDisc on Windows can look for and fix some disk directory corruption issues it is equivalent to the newer chkdsk introduced with Windows XP, the equivalent on a Mac is 'Disk Utility' in your Utilities folder in your Applications folder. A third-party tool which goes even further is 'Disk Warrior', this rather than repairing a damage disk directory builds a new fresh and undamaged replacement. Disk Warrior by building an entire new disk directory also optimises the directory as part of this process.

While Disk Warrior optimises the new disk directory it does not do a full-blown disk defragmentation. To some extent this is a function built-in to OS X and totally automatic however it only applies to smaller files. See Disk Utility 12.x: About disk defragmentation and http://macs.about.com/od/faq1/f/defrag.htm

Note: The disk directory is the list of files on the disk and where they are located on the disk.