I would consider the following:
Nomenclature (naming convention)
Placement (are documents in the correct category/subcategory)
Document Dates (do they use date created or version date)
Business Version (are all versions present, if applicable)
Missing documents (if there is an IRB approval, there should be a submission)
Mapping process (if a document is at 4.1.2 in their system, will it still be at 4.1.2 when transferred to your system)
Proper scanning (are pages in correct order, are they cut off, are they legible)
Are documents in PDF or native format (depending on your sponsor requirements)
Are there are any password-protected documents
Are there documents with other documents embedded in them
Do emails have attachments connected or separate