The feature called 'Enable access for assistive devices' is found in the Universal Access preference pane. It needs to be enabled in order for any GUI AppleScripts to run. I was trying to enable it from the Terminal, to insure that it was always enabled when needed. I struggled with this for a long time, and then finally found a simple solution.

To turn it on, type this in Terminal:

sudo touch /private/var/db/.AccessibilityAPIEnabled

To then disable it, type this:

sudo rm /private/var/db/.AccessibilityAPIEnabled

Thats it. If you wanted to AppleScript it, you could do something like this:

do shell script ¬
  "touch /private/var/db/.AccessibilityAPIEnabled" password "pwd" ¬
  with administrator privileges

[robg adds: Somewhat obviously, replace pwd with your admin user's password. Also, change touch to rm for the opposite version of the AppleScript.]