In Dual Mode if you hit Enter to edit a file name on the right window, edit it and try to select another icon from the left window to edit it using Enter, the icon on the right is the one being edited, both are selected, but the file name being edited is not the correct one.
Open two tabs, double click on one of them to enter Dual Mode, try to double click one of them again to exit Dual Mode, it exits Dual Mode, but the window hides from view.
I was unable to reproduce your #2 on pristine 10.9.2 system. Tried both settings in Dock.
btw. this revealed another issue - when you DO have checked “Double click a window’s title bar to minimize” then double-clicking tabs will cause whole window to minimize.
Everything is working fine now. BTW, this update checked the “Disable tabs completely” setting, I had to uncheck it and restart the Finder, no big deal, but this is the only setting that changed from my TF preferences.