How do I compile vim with the --enable-gui=yes flag on OS X 10.8.2
You can fix the error about missing header files by exporting CFLAGS like this before running make:

export CFLAGS="-I/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.7.sdk/Developer/Headers/FlatCarbon/"


Unfortunately, a new attempt to compile vim fails with loads of errors:

/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.8.sdk/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/CarbonCore.framework/Versions/A/Headers/MacTypes.h:17:24: error: #include nested too deeply
(...)
/System/Library/Frameworks/CoreFoundation.framework/Headers/CFBase.h:156: error: conflicting types for ‘Boolean’
/usr/X11/include/X11/Intrinsic.h:155: error: previous declaration of ‘Boolean’ was here
(...)
/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.8.sdk/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/CarbonCore.framework/Versions/A/Headers/MacTypes.h:11:20: error: missing binary operator before token "("
(...)


and README_mac.txt doesn't offer much help:

(...)
Sorry, this text still needs to be written!


After some more failed attempts with other compile options, and after skimming through the errors, one quickly gets the impression that GUI support is not yet implemented for OS X, at least for Quartz. 

A look to the other options for getting vim, HomeBrew and MacPorts, pretty much confirms the suspicion: The former doesn't offer GUI support at all (see here) and the latter only using X11 (see here).

So to compile vim with GUI support you will have to revert to the good ol' X11 (I tested the Athena widgets, other options are motif and, if you use GTK, gtk1 and gtk2):

$ make distclean
$ ./configure --enable-gui=yes --enable-gui=athena --disable-darwin


After launching XQuartz I could start vim in GUI mode:

$ export DISPLAY=:0
$ ./src/vim -g




However, I have the impression that this is not the GUI support you need to embed vim inside Eclipse.