+1 on the last issue. (LoL launches off-center)
Borderless Windowed @ 2048x1536 (Same as desktop resolution of that monitor)
Triple Monitor Setup
NVIDIA GeForce 9600 GSO on two monitors, integrated ATI 4200 on the last.
Game launches offset towards the left and right, similar as the picture posted by the OP. This is very similar to the previous reported issue of borderless windowed launching offset to the bottom right, off screen.
How to reproduce: Play a game, pray it launches centered. Sometimes it won't. In my case, it was a practice game.
Not sure if this is the same issue as the OP (His first issue).
Symptoms: LoL appears to be the "in focus" application (LoL Cursor is shown as opposed to the default white Windows Cursor). However, when attempting to move the mouse to the edges of the screen (to scroll around the map) the borders of the application window are ignored and the mouse flies off screen.
How to reproduce, not 100%:
During loading screen, Alt tab to a different application. Game loads, use the mouse button to regain focus on screen.
This might be patched, since I had this issue only for the previous two patches. But I figure I'd post it anyway since it may be similar to what the OP is experiencing.