The binary depends on libpng12, which is long outdated. Please update it so it can be used more easily by people with current software.
The makefile is constructed brittly as well. It assumes /usr/local instead of using both /usr/local/ and /usr/. It also uses hard-coded paths for wxWidgets includes/libs/flags instead of using wx-config where appropriate. This means I had to spend twenty minutes working out how to fix it to get the right library and include paths in a general case.

Once I tweaked the makefile enough to get it started compiling, it gave a compile error. Actually a bloody load of them.

It would appear you can't implicitly convert a C++ string to a wxWidgets string on Linux. I hacked on ui.h until it compiled (though it probably has bugs with utf-8 strings given that I fixed it quickly and without knowing much of wxWidgets) and then realized this error is all over in the source code and gave up.

This software is an interesting idea, and I'd like to see it work properly on a normal linux install. Hopefully these problems can be fixed.

The problem is with the way you (or whoever built your binary package) built wxWidgets.. if you use --with-stl when you configure it, the std::string<> thing won't be a problem.  If you read that post you linked to it's just someone not using it correctly; it's just an option in wxWidgets.