How can I remove duplicate second Unity Launcher on a Dual Screen setup?

You can now.

Open up Display preferences, and then you can choose between having the launcher on one display or all of them.

This dialog also allows switching on or off the sticky edges (i.e. the mouse slowdown) between the displays.

The slowdown is a feature to make it possible to use the launcher when it's set to auto-hide. I think it's a bug that it's used when the launcher is set to always visible. I've reported it on Launchpad.net, where bugs are filed, and you might want to set it to affect you. You can find it here: https://bugs.launchpad.net/ubuntu/+source/unity/+bug/945847

In the meantime, you can configure it yourself by using /apps/compiz-1/plugins/unityshell/screen0/options/overcome_pressure and /apps/compiz-1/plugins/unityshell/screen0/options/stop_velocity in gconf-editor

You can also configure these parameters in CCSM (Compiz Config Settings Manager), in the Unity Plugin, Experimental tab

I just found a setting in gconf-editor that will allow you to set the launcher to just your primary desktop: /apps/compiz-1/plugins/unityshell/screen0/options/num_launchers. If you set it to 1, the Unity launcher will only be displayed on the primary desktop. If you set it to 0, the launcher will be available on all desktops.

In addition to this setting, I also set the the overcome pressure (/apps/compiz-1/plugins/unityshell/screen0/options/overcom_pressure=1) and stop velocity (/apps/compiz-1/plugins/unityshell/screen0/options/stop_velocity=20).