If you are using more recent versions of the plugin (say, 0.9.x and later), semantic analysis has been added to the plugin. It doesn't do everything that you want (yet), but it does detect many types of errors, and, to answer your example, it does attempt to find type errors and access errors as well. Determining type is hard, so that code is a bit buggy. You can install the latest plugin directly from inside IDEA via the File->Settings->Plugins dialog. You can find more instructions at the project page:
http://intellij-haxe.org/wiki/installation