I just did some testing with a viz I have embedded into SharePoint 2010 with the page viewer webpart. The multi-value drop down shows all the values. However, when I reduce the vertical size of the page viewer webpart, the size of the multi-value drop down is limited to the size of the webpart. It will not show outside of its defined boundaries. This makes sense to me because it is essentially like an i-frame, and doesn't know if any screen real-estate exists outside of its own boundaries.
Thanks. To be super clear on what we are seeing, belowis a screen shot with the cut off filter on the right. You can see three items but really there are 50 in the list. The page / webpart in sharepoint seem be to sized appropriately - there are no veritical or horizontal scrollbars on the dashboard itself. Are you suggesting that even what that, we need to make the webpart bigger to solve this issue?
With so much redacted, it is difficult to tell what is happening. Is the box below the drop-down in question a Tableau object? If so, I am unable to replicate your behavior in SharePoint 2010/Tableau 8.1. On mine, the drop-down size is only limited to the size of the webpart, and shows above or below, whichever is larger.
Sorry I can't be of more help.