What should I do about a bad professor?

I suggest going to the department secretary. In every department I have been involved with, this is the person who handles the mechanics of things like getting profs to submit a syllabus, grading scheme, calendar, and so on. Simply ask

Do you have the [missing item] for [course] by [prof]?

If you thus receive what you want, mission accomplished. If the answer is "no, I understand [prof] was going to hand them out in class" or just "no" you can go on to

We didn't get them in class and I have emailed and asked for them but no reply.

Typically at this point the secretary will swing into action. I've seen profs called while students are standing there, I've seen heads visited, emails sent, all kinds of things. This is what this person does and the ones I know all do it very well indeed.

If the secretary just kind of stares at you in a "sucks to be you" way, you could try

Is this something I can raise with [head] because I have no idea what the class schedule looks like and only a very vague idea about how grades will be calculated.

You will now get a yes or a no, if it's yes the secretary will set you up an appointment, if it's no then you need to ask why, take notes, say thank you and leave. After you leave the office check to see if you have an Ombud or someone in Student Services who can help you. But I actually doubt it will come to that.