Once in a while there a tiny empty window shows up. Its name is "VSN LogicUIWnd" and shows up in the task bar. When right-clicking on its icon on the taskbar it says "VAIO Smart Network". How do I get rid of this? Is it safe to uninstall VAIO Smart Network? It is annoying because it's yet another window that I have to go through when moving from window to window using ALT+Tab.
VAIO Smart Network utility is Sony's utility to manage your network connections for you. You don't NEED it, however you may have gotten used to using it to connect to your wireless network(s) or use different profiles for different networks.
Windows can itself manage your network connections quite handily, so yes you can uninstall VAOI Smart Network without any adverse effects. You may need to become accustomed to using Windows's built in network tools, however those are easy enough and self-education enough to where that shouldn't be a huge worry.