Having the same exact problem.
I upgrade from OS 10.6.8,( which was running Filemaker 12 Server 184.108.40.2067 successfully), to OS 10.8.2 which doesn't show port 16000 and can not launch the Admin Console. Luckily, I used Carbon Copy Cloner and cloned the entire HD so I was able to go back to OS 10.6.8. Port 16000 shows up in OS 10.6.8 so I know it isn't with any router network settings. I'm thinking about un-installing FileMaker 12 Server then re-installing it in OS 10.8.2. Maybe during the installation process Filemaker opens that port some how.
I sent an email to Filemaker for advise before actually doing this. I'm hoping they will send me an easier fix. I'l post the results. If you've gotten it fixed please post what you did.
I ended up reformatting and installing OS X 10.8.2 (Server) fresh, along with a fresh install of Filemaker Server 12. Everything installed properly and Admin Console started up just like it should've to begin with. There must be a glitch in the upgrading process somewhere on Apple's part or Filemaker's part. Wish I knew what it was, but wanted to follow back up and let you all know what it took to get it working again.
Thanks Sage, I kind of thought that might be the case. I'm going to try and just do a fresh Filmaker Server 12 install first and see if that works. Hate to do a reformat and OS install. Still no inpout from Filemaker too :-(