Someone started an automatic update of the WP core via dashboard today, and as it was taking too long, decided to cancel it. How do I check the files and the database for integrity to detect a possible corruption?
Check for files and database integrity
From development point of view the most practical way to detect and locate changes is version control – comparing against SVN/Git checkout of core or use such checkout directly.
However there are also plugins around that verify files against set of hashes. I think Sucuri Security recently got such feature. The practical limitation of them is for which versions hashes are provided and how fast are they updated for new releases.
For database there isn’t quite any easy method (not counting native MySQL functionality). On other hand WP doesn’t do much to database on updates nowadays and it comes as separate explicit action (via splash screen) after file update was performed. From you description process probably hadn’t reached that point and no changes to database were attempted.