Bad news... Without updates from Finale, I doubt it is possible. The error you received is an Exception, which is a possible error not considered during the software development phase. When the software does not know how to handle an error, it crashes wildly, resulting in this "Exception unhandled". It is probably due to the fact that in Yosemite, some paths or libraries that Finale looked for by default are no longer in that position or no longer exist; not knowing how to handle the problem, the software crashes.
The only solution, unless there is a bug fix update from the manufacturer's website, which I recommend you check, is to perform a downgrade using Time Machine to the state prior to the OSx Yosemite update.
Regarding operating system updates...
For those who work with a Mac, it is always discouraged to move to more updated operating systems unless there is an extreme necessity.
In more updated systems, sometimes, the improvements made are mainly at the level of Frameworks for developers. Unfortunately, however, some third-party applications are no longer compatible with older systems, and therefore sometimes one must yield to the OSX update. In any case, before updating, it is always advisable to check with a simple Google search whether our third-party software is compatible with the new versions of OSX; otherwise, it could be a problem, as in this case.
The steps for the solution are those I told you. Before performing the downgrade, try contacting the Finale developers to ask if there is a bug fix, perhaps by sending them, if available, a debug log that the operating system usually releases when these exceptions occur, and wait for their response.
If no bug fixes exist and they tell you to move to a more updated version of Finale, such as 2014, you can choose to update the software or perform the downgrade. The only way to perform the downgrade is through the use of Time Machine. I hope you have a recent enough backup to resolve the problem; otherwise, you will have to format and reinstall an older operating system from the installation discs provided with your Mac, or by purchasing a Retail version of the operating system you were previously using from the Apple Store, proceeding with a formatting and reinstallation of all third-party software.