Is the pickling process deterministic?

I suppose there could be a gotcha when pickling dictionaries that have the same contents but different insert/delete histories.

Right:

>>> pickle.dumps({1: 0, 9: 0}) == pickle.dumps({9: 0, 1: 0})
False

See also: pickle.dumps not suitable for hashing

My goal is to create a "signature" of function arguments, using Pickle and SHA1, for a memoize implementation.

There's a number of fundamental problems with this. It's impossible to come up with an object-to-string transformation that maps equality correctly—think of the problem of object identity:

>>> a = object()
>>> b = object()
>>> a == b
False
>>> pickle.dumps(b) == pickle.dumps(a)
True

Depending on your exact requirements, you may be able to transform object hierarchies into ones that you could then hash:

def hashablize(obj):
    """Convert a container hierarchy into one that can be hashed.
    
    Don't use this with recursive structures!
    Also, this won't be useful if you pass dictionaries with
    keys that don't have a total order.
    Actually, maybe you're best off not using this function at all."""
    try:
        hash(obj)
    except TypeError:
        if isinstance(obj, dict):
            return tuple((k, hashablize(v)) for (k, v) in sorted(obj.iteritems()))
        elif hasattr(obj, '__iter__'):
            return tuple(hashablize(o) for o in obj)
        else:
            raise TypeError("Can't hashablize object of type %r" % type(obj))
    else:
        return obj