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In Alfresco Share, is there a way to track who's read/previewed a document and store that in a datalist?
well, have you seen the activity dashlet? if this is not sufficient you might want to consider auditing.
You need to enable auditing for your Alfresco installation.
http://docs.alfresco.com/community/concepts/audit-intro.html
To view audit logs, you must setup Alfresco Audit Dashlet or a custom audit viewer module.
https://addons.alfresco.com/addons/audit-dashlet