A [Terminator] (https://launchpad.net/terminator) plugin for 1-click dumping of the console contents to a text file (~/.terminator/$datetime.log)
One needs to copy the plugin to /usr/share/terminator/terminatorlib/plugins/ and enable it under preferences to make the context-menu (named "DumpToFile") appear. Dump files are stored under ~/.terminator
For Gtk3 versions of Terminator (ver 1.90+) use the terminator-1.90 branch here.