UPDATE: Apple has released an OS X update to fix the application crashes.
Apple has released OS X update 10.10.1 to address the application crashes caused by the finder integration. This update is available for free in the Mac App Store. Details on how to update your Mac are available on Apple's support site.
Apple’s OS X Yosemite 10.10.0 causes some programs to occasionally crash when they display an Open, Save, or Save As window. If a program crashes before you’re able to save files or changes, the work you’re doing won’t be saved and may not be recoverable.
These crashes can occur when any application—like Dropbox—uses Yosemite's official mechanism for integrating with Finder as well as with Open, Save, or Save As windows.
The Dropbox desktop application disables Finder integration on OS X 10.10.0 by default to prevent these crashes from happening. Finder integration is not required to sync files; however, it is responsible for displaying the sync and status icons on your files, as well as for the Dropbox menu options available through right-clicking on files.
If you're running OS X 10.10.0, you will need to update to OS X 10.10.1 or later for Dropbox to function normally. This update is available for free in the Mac App Store. Detailed instructions on how to update your Mac are available on Apple's support site.