As noted in "Building and Deploying Flex2 Applications" (Live Docs), the output of trace statements can be configured in the standalone debug version of the Flash player. The documentation describes the location of the mm.cfg file on Mac OS X using Mac-style (non-Unix) path notation with colons to separate directories.
I set up a config file, but for the life of me, I couldn't find the output file. Then, I found an old, pre-Flex2 blog post by Christian Cantrell which fills in two missing parts of the documentation. First of all, if no TraceOutputFileName directive is given, the trace output will go to flashlog.txt in the same directory as the config file - fair enough. Once I removed the directive, I found the output file.
Also, if a path name is given, the path must be specified in the old Mac-style notation (with colons) rather than Unix-style (with slashes). I suppose that's why they specified the location of the config file in that notation, but the significance of the colons was lost on me. One totally trivial tidbit correctly noted in Christian's blog post is that the directory name is "Macromedia" not "macromedia", as indicated by the docs. (Since the Mac's HFS+ file system is basically case insensitive, it doesn't really matter.)
Once I figured that stuff out, I could get my trace output and get on to fixing my bugs.
I do have (at least) one gripe with the debug Flash player on the Mac compared to the PC - it doesn't keep a history of recent URLs. So, every time you go to open an URL, you have to type it in again (or paste it from a browser, which does keep history.) Even if you keep the player running, it still doesn't remember the last URL it opened.