Something breaks duing 'make'. Where should I look first?

First of all, check the GTK+ FAQ. Since gtkmm is built on top of GTK+, they share some common dependencies, such as a proper version of Perl and a fully functional (GNU style) make. If you've managed to successfully compile GTK+, you know that the basic parts of your C compile environment are OK and you can start to focus on the C++ side of things.