4) Myabe allow to speed my code up (JIT), or make Python as fast as possible. But this is rather a long term goal. Generally, I don't see why my code written in C and the same code written in Python, not using much dynamic features, couldn't be the same fast. (Of course I understand why now it is slower, Python is interpreted, etc. But I mean in principle. Python can have as much information about my code as the C compiler.) I use Python for devising new numerical algorithms, and than I need to rewrite them by hand to fortran for speed. It's a pain.
6) Allow efficient threading? CPython has the GIL (for good technological reasons). Generally pypy can improve how to do things in parallel in python. Currently, one needs to use pympi, pypar, or something.
These two together are, in my mind, where PyPy can really shine. Performance on par with CPython is critical to be taken seriously, but CPython's difficulties with the GIL mean I can only make it scalable at about 60% to 65% of the traditional efficiency (on pystones at least). That gap gives PyPy enough room to surpass CPython on scalable performance. -- Adam Olsen, aka Rhamphoryncus