The overlay in Baseliner 1.0 now indicates it does not want to be a target of mouse events. When Baseliner is open, it’s possible to interact with the page beneath.
The bookmarklet has been updated to use 1.0. This version has been tested in the latest Safari, Firefox, and Chrome on OS X 10.10. Baseliner 1.0 is enabled on this page, so you can test whether it works in your browser of choice.