Ahoyhoy,
There is now an `inferior-slime-mode'. This is a minor mode to use with inferior-lisp-mode, i.e. in the *inferior-lisp* buffer. It's like the normal slime-mode but with fewer keybindings, e.g. it doesn't have M-p and M-n because a) there're no compiler notes in that buffer and b) comint uses those for input history.
I was pretty generous in adding slime-mode bindings to this new mode, though some of them are shadowed by inferior-lisp-mode (probably rightly so). Some tweaking may be in order.
The README is updated - what you need is:
(add-hook 'inferior-lisp-mode-hook (lambda () (inferior-slime-mode t)))
Thanks to everyone who pointed out the problems of using the regular slime-mode with the inf-lisp buffer.
Cheers, Luke