Two things bothered me about the desktop application - it runs as a Chrome application rather than in a tab (not sure if there is a technical reason for this?). If I care enough out privacy to run Signal then I probably don't want to broadcast to anyone watching my screen that I'm running it (like a boss walking past etc) and would rather bury it amongst my other open tabs. I also couldn't find any obvious way to sign out of or lock the desktop client - if this isn't just user error then it seems like a significant oversight for a secure messaging app to not allow the user to control access if someone else was able to access the computer.
It also really bothered me that signal doesn't give me better control over what contacts can see my phone number. When I signed in I could see phone numbers for a contractor I had used for remodelling my home. The desktop client had them listed as someone to message on the default page. It's not a huge deal in this situation but if the phone number was for someone I no longer wanted to be in touch with (a former partner etc) then there was no obvious way in either the Android app or desktop client to block them. I assume that the other user can also see my details - security should include having control over who can see your phone number.
Edit: Screenshots from the desktop app as a response to comment below:
http://imgur.com/5nK07ER - the default screen http://imgur.com/mmEyQWH - the settings UI
http://imgur.com/gjdyPsF - showing Signal in my dock for all to see.