I've been experiencing this for a few weeks too, and have finally done a bit of digging on this...
Cause
The Mac firewall checks that applications have been 'signed' properly before allowing them to receive incoming connections. Code signing is a digital certificate that validates that software has been written by a trusted author, and has not been modified in any way.
Unfortunately, there are a couple of components within Finder.app in the 10.10.1 release that haven't been signed properly!
We can see this by firing up a Terminal window and issuing the following command:
codesign -vvv --no-strict /System/Library/CoreServices/Finder.app
You'll see a message that a "sealed resource is missing or invalid" because a couple of files have been modified...
I am guessing that Apple tweaked these files at the 11th hour and didn't get them signed properly, though it is also possible that a third party app that uses Finder extensions (I use the cloud drive app "Egnyte" for example) has modified them (though I think that's unlikely). Is it possible that this issue isn't more widely know because most people aren't using the firewall? (It's off by default)
Solutions?
1. I've seen a crazy recommendation to 'Show Package Contents' for the app, and simply delete the offending files... I'd strongly advise against that 😉
2. It's possible to codesign Finder.app yourself by generating an author certificate, updating your keychain so your system trusts apps that you codesign, and then signing Finder.app. Hmmm, it's difficult to recommend this route as well - it is a complex process and may introduce issues further down the road when the next OS update comes our way.
3. Sit tight for now, keep hammering that "allow" button (or turn off the firewall if it kills you that much) and wait for the next OS update which hopefully has Finder signed properly...
I'm sticking with option 3!
HTH,
Dan