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.
We’re in touch with Apple and are working together to resolve this quickly, but don’t yet have a timeline on a fix. We’ll be updating this post, our blog, and Twitter at @dropbox_support with the latest news.
This issue only affects Macs that have OS X 10.10 Yosemite installed and have installed the Dropbox desktop client. This does not affect users running OS X version 10.9.5 or lower. To see which version you're running, follow these steps: