Consider the following:

from functools import singledispatch

class Dispatch:
    @singledispatch
    def foo(self, a):
        return a

    @foo.register(int)
    def _(self, a):
        return "int"

    @foo.register(str)
    def _(self, a):
        return "str"

cls = Dispatch()
cls.foo(3)  # 3
cls.foo('hm')  # 'hm'

I find this quite unintuitive. Essentially, since singledispatch dispatches based solely on a functions first argument, it is useless on methods unless one wraps it and modifies how it uses the internal wrapper function. I believe this should be relatively easy to fix with adding a check of inspect.ismethod and then modifying the number of the checked argument where appropriate.

I'm happy to write a patch if this change is seen as a good idea.