I have BibDesk 1.6.3 running on OS X 10.9.5. I tried "Check Updates" and it offered version 1.6.5. However, when I tried to install that update I got an error saying "Update Error! This update is improperly signed."
I declined to install the update.
I have not heard that, and 1.6.5 is out for quite some time. Perhaps soemthing went wrong with the downoad. Have you tried the downoading from the site?
OK, I tried again from a different network and it worked.
So there was something wrong with the download. I had tried multiple times and waited about 20 minutes between tries. Not sure why it would have failed as I was able to successfully update other tools like LaTeXit from that network at that time.
This bug can be closed/rejected.