I just added this as a post on my blog and thought it might be useful here too:
I am using the AlterDialog.Builder to create my dialog (see code below), however this method will work with all kinds of dialog providing you can access it via getWindow.
Below shows the code needed to add blur and remove dimming of the background (as I think the blur looks nicer when the background is well lit).
The blur is simply created using the last line (line 4) which sets a flag for the dialog telling android that we want windows below this one to be blurred. To achieve the dimming, we need to retrieve the layout parameters for the dialog window, set the dim amount to zero, update these parameters with setAttributes (lines 1-3).
See below for a screenshot of this in action: