This error results when there is a merge field on the Word template that is formatted as a date (e.g. \@ "MMMM d, yyyy") while that field in Salesforce is not a date field (e.g. instead it's text). The error results because Conga cannot format a non-date field as a date.
What to do
To fix the error, start by toggling all field codes on Word template (Alt + F9). Look for non-date fields that are formatted as dates. Beware, as some fields that sound like date fields (e.g. Deliverable Due Date) are in fact not. When you find the merge field in question, delete the date formatting (e.g. @ "MMMM d, yyyy"), right-click the field and select "Update Field." Alternately, you may delete the entire merge field and simply re-enter it without any date formatting.
The error may appear when merging from some records and not from others. This is because the field in question is not populated on the records where the merge works.