I understand that Django, PyPy, and Psycopg2 all work correctly together, and speed.pypy.org claims great performance improvements over CPython. Are there any downsides?
Library support. Not all libraries are compatible with PyPy.
Your best bet is to actually try running pypy manage.py test
and see if it breaks. Then you know which dependencies need to be brought into line.
http://reinout.vanrees.org/weblog/2011/06/06/django-and-pypy.html
Webservers
You can't use pypy with Apache. You need to use a pure-python webserver + nginx. You MAY get it working on uwsgi.