Thank you for the post.
This was previously reported by other user's in the following thread:
FileMaker 10 and earlier versions of FileMaker have not been tested or certified with Mac OS X Mountain Lion. These products were developed and released before Mac OS X v10.8 Mountain Lion became available.
While these earlier versions may install and run on Mac OS X v10.8 Mountain Lion, you may encounter installation and stability issues for which there is no resolution. We strongly recommend you use current FileMaker software.
The full knowledge base article Answer ID: 11007 can be found at the following url:
At the time of this post, the full 30-day trial of FileMaker Pro 11 and FileMaker Pro 12 are available for download here:
I don't wish to speculate on the particular setup of your environment, but in most cases a good starting point would be testing with the most up to date version of either FileMaker Pro 11.0v3 or FileMaker Pro 12.0v3. Please let us know the results of your testing, as that information will help others seeking similar answers.
Click the last hyperlink to see additional information on versions tested to be compatible with Mac OS X 10.8 Mountain Lion.