Bug 1: Sometimes the homepage in L5 will get stuck with the little loading circle continuously going around, and therefore the homepage won't load. Never had this kind of problem in L4.
Bug 2: I think I remember reading awhile back that people were having quit problems with L4. I also had those problems, and have noticed they have stuck around with L5. I am frequently required to force quit because the app does not like to quit properly on its own.
That coupled with the homepage not loading, and the fact that sometimes the app simply gets stuck at the gray loading boxes, makes it seem as if the app has trouble both starting and stopping. Seems like a pretty basic problem that should be addressed.
Used L4 Mac, and am using a Mac with L5, by the way.
On the homepage issue the windows command I have used in the past to fix this is Shift-F5. I am not sure what the Mac equivalent would be.
Logs would probably help the developers see what is happening http://wiki.logos.com/Diagnostic_Logging
Logging Tool
Have never experienced either problem with L4 or L5, but you might try Fred's suggestion. I know F-5 works to refresh the Home Page in both versions, so perhaps this will also work the same.
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