According to Jalkut, apps, like his own MarsEdit, throw an error involving the CoreSchedulingSet or EmptyCoreSchedulingSet C++ objects when trying to connect to some network resources.
Working with the folks from Agile Bits, Jalkut traced the problem to the Auto Proxy Discovery and Automatic Proxy Configuration settings in the Network preference pane. Under most circumstances, these options would not be turned on; the exception is in large institutional or corporate networks where specifically required by the network configuration.
If these options are selected in the Network settings, then you may experience this crashing problem with apps that rely on Apple's networking libraries. These apps include, but are not limited to, MarsEdit, Tweetbot and Safari.
Jalkut recommends that Mountain Lion users turn off the Auto Proxy Discovery and Automatic Proxy Configuration features until Apple issues a fix. You can read more about the networking issue and instructions on how to fix the problem on Jalkut's Red Sweater blog.