Hi Susan:
There are 2 parts to a Data Integrity Check: File Integrity and Application Integrity. I'll describe the 2nd one first because it is easier to visualize.
The Application check looks to make certain that the data "matches". Here are a few examples: Does the total of outstanding invoices for customer ABC match the total on ABC's master customer record? If customer XYZ is assigned Terms code "NET30", does that code still exist in the master Terms list? Is every record in the Ship To table matched to a customer in the Customer master? Are there any Sales Orders without a matching customer in the Customer master? And so on.
When these errors are detected they are generally listed in the on-screen log (though more detail and clarity would always be welcome). This is what you encountered on Oct 1.
The File check looks at more fundamental problems. Does the index match the data table? Do the correct data tables exist? Support could explain better what happens during this check.
These errors are not so easy to describe. As a result they aren't always listed in the logs (on-screen or otherwise). This is the situation that you encountered on Oct 2. As Andrew said, you have probably lost absolutely nothing. However it would be helpful if more detail was logged (and a "Print" button placed on the Data Integrity screen to list the log file).