As a side note, the ODBC driver/DSN definition is working OK as I can do an "File->Open" and give it a SELECT query to bring in data rows from the MySQL databse. I can also use Excel to get data from this ODBC source.
Still not an "ANSWER" per-se, but I also noticed that the FIle-Open and Import steps apparently are "broken" in that they show the table names but not any columns. Again, hand-entering an SQL works here, but not for the relationship graph where it has to construct these statements itself.
One more data point, though... I installed an SQLite3 ODBC Connector from here: http://www.ch-werner.de/sqliteodbc/
It is not supported in the relationship graph, but when I use that ODBC connector in File->Open or Import I do see table names and can use the tools in FileMaker to build the SQL statement instead of having to type it all by hand.
Ok, seems this is, after all, a bug in the MySQL connector. I had tried 5.1.8, then compiled 5.1.9 myself and yet got a different error. Although other programs are using it fine, apparently something with how FileMaker is using it causes problems. I just downloaded the last 3.51 series connector for the Mac and it seems to be working.