"Places" case solved. What I obeserved in short:
At startup, "Places" is created and provides shortcuts to standard folders: Home, Documents, Downloads, Music, Pictures, Video, Network and Root folder. These folders can't be deleted from there (no trash can symbol).
This list is expandable with any folder. These are removable, too (trash can symbol on swipe right).
"Music" folder was deleted. "Places" tried to provide a link to this non-existent folder which ended up with a ".".
"Music" folder was recreated and appeared at the bottom of the "Places" list while "." still existed.
After a reboot, "Places" got organized again (or rebuild by scratch). "Music" folder could be referenced again and "Places" was rebuilt as intensioned and looks normal again.
No "." for a folder that could not be found.
Sorry for causing this inconvenience. It happens, when you're chronically overworked.