Credit goes to Sam Bruce for posting this workaround at the thread above.
I have been moving some workbooks from embedded extracts to published data sources on Tableau Server. Upon converting to Published Data Sources, I noticed all quick filters would default to multi-select lists on every dashboard except the first.
As a workaround/fix, I found the above thread, which stated that if you click on each sheet before publishing your data source, and then replace your data source, all quick filters will retain their respective options, etc.
Very nice! I've been wanting this for a long time, and didn't realize there was a good work-around. Posting this in hopes that others will find it as useful as I have!
2/28/14 UPDATE: This issue appears to apply to any scenario that involves replacing a data source. Touching each worksheet before editing the connection info, or replacing a data source, will retain quick filters across all sheets.
More info here--Credit goes to Shawn Wallwork for testing this on another scenario: Edit Connection Empty Filter Issue...