Many users compain that the unity launcher doesn't show when cursor is moved to the left edge of the screen in Ubuntu 12.04. Many of them reported this issue as a bug, but it is a feature instead. Some tries to push mouse cursor hard to the left hoping that unity launcher will appear, but without success. The trick here is not how hard the mouse cursor is moved to the left screen edge but how far (or fast).
If you've read our post how to enable unity launcher auto hide in Ubuntu 12.04 Precise Pangolin you could notice that we've mentioned that you have ability to configure unity launcher reveal location and also configure sensitivity. But sometimes it is not enough to satisfy your needs.
Here are the steps that could help you in using the launcher in the way you like:
1) Install CompizConfig Settings Manager (known by its shortname CCSM)
2) After the installation, start CompizConfig Settings Manager
3) Go to Desktop > Ubuntu Unity Plugin > Experimental tab
4) Find the option "Launcher Reveal Pressure"
5) Default value is 20, but you can change it to any lower