What is the quickest Mac OS X app to use to remove the background of an image to make it transparent?
Just selecting an area and hitting delete just as you do with the Alpha tool should do it fine.  I tend to get a good outline with the alpha tool, then zoom in and use the lasso selection tool to draw around any stray pixels - remember to complete the lasso yourself, or it may complete it for you and if the end is not near the start, it will just draw a big line between the 2 across whatever is in its way.

You don't say what OS you are using, but I've done it this way in every OS since Tiger...