Anyway, I just discovered a very easy way to get around this apparent limitation. My solution does not involve having several copies of Blender, but rather using the Terminal to open multiple copies of the same Blender application. Yes, the Terminal, that little known utility that scares most Mac users out of their wits, or at least it used to have such an effect on me.
There are two things you need to know about the Terminal. First, you can navigate to any folder in your Mac from within a Terminal window. To do so, you open a new Terminal window, type cd (which stands for change directory,) and enter the name of the folder or file you want to have accessible. After that, just press Enter. The Terminal allows to autocomplete file and folder names by pressing Tab. To make sure you are where you're supposed to be, type ls (for list) and press Enter. That shows you the files in the folder you are viewing. You can type an entire path to a specific folder or file by separating the folder inside folders with a /. To backtrack, type cd .. (that's two dots) and press Enter. To go to the root user folder, type cd ~. These basic commands will allow you to start navigating your Mac from the Terminal.
The second things is that you can perform commands from the Terminal. You can open programs and files, edit them, save the changes. Actually, it can do this and more, but at least it is important to realize that you can open a program from the Terminal. In order to work on a file, you need to navigate to the folder where that file is contained—in the same way that, in order to open a file, you need to go to the folder and double-click on its icon.
Once you can do that, go ahead and start a new Terminal window. Navigate to your Blender application folder. Yes, what we see on the Finder as Blender is not a program, but a package: a special Mac folder that contains the program itself and other files used by the program, like the icons, scripts, and default file. Anyway, navigate inside your Blender package, all the way to the folder where the actual program resides. If you have Blender in the main Applications folder in your Mac, the path to it would be (assuming you start from your user folder):
cd ../../Applications/blender/blender.app/Contents/MacOS/Then, once you're there, open Blender by typing
./blender
The terminal spews out a couple of unintelligible lines, which I choose to ignore:
ndof: 3Dx driver not found
found bundled python: /Applications/blender/blender.app/Contents/MacOS/2.60/python
[Lux 2011-Dec-11 13:37:01] Using pylux version 0.9 (dev)
In any case, the end result is that you get a new Blender window open, independent of the other(s), and it allows you to work with two files at the same time! Cool stuff. I would suggest saving this text somewhere, either as text or as a script, so that you don't have to enter it manually every time. If I work out a Python script for this, I'll make sure to share it.
Enjoy!