As a reply to my own question #5 in corresponding thread  I found this Admin Tools  set of scripts.
I have run Admin.SanityCheck and found that I have
10 records of DOCUMENTS: checking for data with bad characters in document name
1 record of ATTACHMENTS: checking for attachment where the document does not exist
6 records of ATTACHMENTS: checking for attachment with no attachment archive
3 records of ATTACHMENTS: select "checking for attachment with no attachment content
137 records of DOCUMENT - Translations: Checking original documents that are marked translated
137 records of DOCUMENT - Translations: Checking orphaned translated document (without an original document)
377 records of DOCUMENT - Check that Parent fields still exist
This seems like not that good statistics and I would gladly fix it, but I don't know how. More over it's not always clear what the issue is and what are its consequences (like in e.g. Document Translations' cases).
Is it possible to extend the script with mentioned above info?
You can reply to this thread explaining items one by one and providing instructions on how to fix each issue and then just gather the info into the script.