I have a Python class full of static methods. What are the advantages and disadvantages of packaging these in a class rather than raw functions?
Depends on the nature of the functions.  If they're not strongly unrelated (minimal amount of calls between them) and they don't have any state then yes I'd say dump them into a module.  However, you could be shooting yourself in the foot if you ever need to modify the behavior as you're throwing inheritance out the window.  So my answer is maybe, and be sure you look at your particular scenario rather then always assuming a module is the best way to collect a set of methods.
Is there any advantage in using a Python class?