When this is written, flash builder 4 doesn’t have a native way that lets you use it, so we have to do a little mix. (Update: The update is out.)
The global error handler works by adding an event to the uncaughtErrorEvents property of the loaderInfo of the application.
There are currently two methods of getting it to work.

Method 1 - The backwards compatible one:

Here the code doesn’t crash in flash player 9/10, but the error handling will only work in 10.1.

if(loaderInfo.hasOwnProperty("uncaughtErrorEvents")){
	IEventDispatcher(loaderInfo["uncaughtErrorEvents"]) .addEventListener("uncaughtError", uncaughtErrorHandler);
}

private function uncaughtErrorHandler(e:Event):void {
	trace("Global error:", e);
}

Method 2 - The type safe one:

Get the Flex 4.1 SDK if you haven’t already and choose that one as your project’s SDK.

Now you can use the new global error handling like it was meant to be used:

import flash.events.UncaughtErrorEvent;

loaderInfo.uncaughtErrorEvents.addEventListener( UncaughtErrorEvent.UNCAUGHT_ERROR, uncaughtErrorHandler);

private function uncaughtErrorHandler( e:UncaughtErrorEvent):void {
	trace("Global error:", e);
}