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).

I solved using disper. Type in a terminal:

sudo apt-get install disper

After solving the issue with the method proposed by Paŭlo Ebermann or nvidia-settings or whatever works for you, type in a terminal:

disper --export < /path-to-my-file/my-disper-file.metamode

my-file.metamode is as follows:

backend: nvidia
associated displays: DFP-0, DFP-1
metamode: DFP-0: 1366x768 @1366x768 +1920+312, DFP-1: 1920x1080 @1920x1080 +0+0
scaling: stretched, stretched
xinerama info order: DFP-1, DFP-0

The third row takes into account the particular positioning of two screens with different heights. Your case may be simpler. You could try to create the file that fits your configuration (without using other methods + disper --export). The important point is the order of the screens in the second and in the last rows.

You can use the script and making it run at startup:

#!/bin/sh
#Auto switch single/extend display with disper on Multiple Monitor.
lines=$(disper -l | wc -l)
display_count=$((lines / 2))
if [ $display_count -eq "1" ]; then
   disper -s
else
   disper --import < /path-to-my-file/my-disper-file.metamode
fi

It worked with my nvidia graphics card (both precise and quantal).

Hope it helps.

I tried the combined settings from above:

/apps/compiz-1/plugins/unityshell/screen0/options/num_launchers=1
/apps/compiz-1/plugins/unityshell/screen0/options/overcom_pressure=1
/apps/compiz-1/plugins/unityshell/screen0/options/stop_velocity=20

That was mostly successful for me. A launcher appears only on the primary screen, and the mouse moves from one screen to the next without undue hesitation. However, I found that the remaining launcher would not reveal without using the super key. This can be corrected by setting the following:

/apps/compiz-1/plugins/unityshell/screen0/options/reveal_pressure=1

BTW this is with NVidia drivers.

Just changing /apps/compiz-1/plugins/unityshell/screen0/options/stop_velocity to 1 fixed the issue for me... I didn't necessarily want to remove the second taskbar, just didn't like the pause when going from one screen to the other.