nexus 7 - My space used and free space doesn't add up

See pic - the numbers don't add up!

^{Screenshot (click for larger variant)}

This is a 16GB Nexus 7 The listed items only add up to a little over 9GB. So 4GB worth of files are missing.

How can I find those missing files?

Answer

If the displayed detailed would be complete, you'd be correct: 1.28G + 7.28G + 200K + 282M + 762M = 9.6 GB total space -- while the summary says 13.24G. Explanation is easy: The details list is not complete. It e.g. misses Cache, temporary files, log files, tombstones, and probably some more.

Where to find those? In the file system, and for completeness this requires root. For some more details, please take a look at corresponding questions by following the tags internal-memory and storage. A good source to start with is the question Something is secretly eating up my tablet memory and I need help finding it.