I got passed the libpng error by installing libpng12 from AUR. Now when I run ./sublime_text I get these errors: http://pastebin.com/NYWSaPSe
It's strange because running "python PackageSetup.py" doesn't produce the same errors. My PYTHONHOME and PYTHONPATH are both correct. Using python 2.7.1 on arch.
EDIT: Ah, you've added that now. I'll do some investigation: could you let me (jps@sublimetext.com) know which distro you're running?
(I'm the author of Sublime Text, btw)