I have a Logitech mouse that has a usb connection.  When I try to shut
down my my computer, it will instead restart itself if the mouse is
connected.  This problem also occurs when my flash drive is connected.
My question is how can I get my computer to shut down automatically
without me having to keep unplugging my mouse's usb connection?

It sounds like when you shut down your computer the device either
doesnt know how to shut down (possably a hardware malfunction), or
your firmware and/or drivers need to be updated.

Since your mouse and flash drive both cause it, make sure you
spacifically check your USB Hub. You may also want to try different
USB ports, and try different devices, like printers, scanners or any
other USB device.

Hope that helps,
-ALL