Some files are missing and I suppose there is a record of when a file was deleted? Is this log file present on every sync client? Is there a special tool needed to read these log files?
There is no log on the client by default but you can enable it:
https://doc.owncloud.org/desktop/2.2/troubleshooting.html#log-files
If you use the activity app, it should keep track of certain activities (depending what you have set up). The trash-bin should also tell you when a file was deleted. The webserver logfile should also contain some information (just look at the logfile when you delete a file) that helps you to figure out who deleted a file.
So, you can’t access the log of what has happened from the web console of the user?
If you suspect problems, you can enable logging for the client. The activity app can also be set to keep track of certain actions (is also shown in the client).