The Galaxy Note 3 features the USB 3 adapter, but will also accept Galaxy S4 (USB 2) cables... they plug into the "right" side of the 3.0 interface.
Once such cable is the Samsung Galaxy S4 micro USB to USB Adapter which provides a full-size USB female port. I've tested a wireless mouse and
keyboard via this adapter (with a USB hub) with very good results. The keyboard buffering is a tiny bit lagged but manageable. There's an on-screen mouse cursor (didn't show in the image below) & the mouse moves smoothly on the screen. Right-click on the mouse is equal to the back soft-button on the device.
There's also a USB-to-HDMI adapter but I haven't tried that one yet.