Printf, please give the attached test version of srcds_osx a try. It will still crash, but when it does it will hopefully give me more information about what's going on.
When you try running this, please add the "-nobreakpad" option to the command line and then copy and paste the output you get. It should look something like this:
As to your second message about what happens when you type 'quit', I can't seem to reproduce that on my 10.8.5 system. The message about the "Shutdown function" is harmless, but the "Trace/BPT trap" is interesting and shouldn't be happening either. I'm not quite sure where that is coming from yet.
A couple of additional questions:
1. What is the command line you are using when running the server?
2. Do you have the OS X Steam client on the same machine as the server? If not, did you copy all the libraries (steamclient.dylib, libtier0_s.dylib, etc) as mentioned in the first post?