VisualVm hangs when started from either the downloaded visualvm.dmg or the zip. It gets to the Visual VM Calibration dialog and then stops. There are no messages in the dialog box nor does clicking the OK button do anything. I can't find any log in either my home or the extracted zip folder when I run either.
From the command line I get
./visualvm Unable to find any JVMs matching version "1.7.0_10+". Found jdkhome=/System/Library/Java/JavaVirtualMachines/1.6.0.jdk/Contents/Home
Any advice on how to diagnose the problem would be greatly appreciated.
It's telling you that you don't have a JDK/JRE with a version of 7 or higher. If you didn't install one, then it won't be there - download it from the oracle website, or install the Open JDK if you require version 7 or higher.
You should also be able to see error messages in the OS X console (but I doubt you'll get more detailed error messages than you already received)