You didn’t answer my question, though (about the logfile). What are the permissions on .procmail/ (the directory), and does .procmail/log exist?
I assume that .procmail/spam.rc exists?
I would set the files to 0600, and directories to 0700, but the main thing is to make sure you don’t have any group writable directories… if ~/.procmail/ is 0775, for example, it won’t work. If the logfile doesn’t exist at all despite being mentioned in your .procmailrc, the problem is most likely related to permissions.