I have two main issues with Logos 4 (beta and non-beta versions) and multiple monitors:
1) (this one has been posted elsewhere) When I maximizes L4 on my 2nd monitor the top taskbar goes black, so you can cannot see the minimize/maximize/close buttons, though if you click where you think they should be they are still operational. See screen shot. 
2) The 2nd issue may be a feature, but I find it to be an issue. When I restore a layout, it not only restores the layout but also L4's monitor, size, and position. For instance, I am a working on a sermon at starbucks, and save a passage so I can come back and work on it later. I get back to my office, hookup my laptop to my 2nd monitor, and pull up L4 on 2nd monitor full screen. Do some other work. Then I try to restore my previous layout. L4 restores the layout but moves L4 to my laptop's screen just as it was when I saved it.
Thanks and enjoying L4!