I am getting the exact same issue. Am using FM Server on OS X Mavericks (13v5) using the Actual ODBC driver for MySQL, and am using version: 5.6.23 - MySQL Community Server (GPL) (also on OS X Mavericks).
I have the database connected properly through the ODBC Manager and hooked up in the External Data Sources of FileMaker. It is properly reading from our Artists table, which has 178 fields. We're able to navigate the records, import, delete, etc. using it in a FileMaker layout/relationship.
However, another table, our Shots table that has 526 fields, is giving the same issues as mentioned in the above post - even when viewing a single field and one record.
I believe that a table with a lot of fields causes the SQL string to be too long. I don't know exactly how FileMaker (or the ODBC driver) works, but my best guess is that it creates a SQL Select statement that names all fields in the shadow table, and then fails because the number of fields makes this statement extremely long.
After removing many "shadow fields" from the shadow table in the FileMaker Fields Definitions, the error is gone and all is well.
Is there any way to extend the maximum length of the SQL statement, or are we hitting a roadblock with the MySQL server itself? Perhaps it's just a setting in MySQL to change, like max_allowed_packet, or something similar?