The Welcome Screen was written at the time of GNOME 2, and indeed is showing its age. The os.system call it makes to launch xdg-open (which in turn launches the default web browser) is a blocking call. Meaning it will turn the Welcome Screen unresponsive till you close the web browser. And closing that would generally also close the Welcome Screen. I'm sure there are other "quirks", but this is the one I confirmed from a quick look in the Python file. So while not strictly a bug, the Welcome Screen could do with an overhaul.
Linux Mint 14 Nadia / 64-bit / Cinnamon