1. Place a Web Content Display portlet on a page.
2. Configuration/Scope/set scope to Global.
3. Go back to the first tab in Configuration, click on the drop-down arrow next to the magnifying glass in the search field.
4. A pop-up with further search options appears.
5. At the bottom, click on the My Sites selector.
Result: Global appears two times (first one is the fixed one, the second one comes from the scope of the portlet). I don't think this has any negative impact on functionality, but it looks awkward and confusing. (for example, customer suspected that it has something with using two portal instances, and two database shards)
Expected: Global should appear only one time, even in this case
Master: not relevant as there is no advanced search drop-down there