You can say "shouldn't have," but not "shouldn't've." Or at least, not officially. Because people tend to clip their words, it is possible that when people say "shouldn't have," it sounds like "shouldn't've." I myself probably do this often, especially when I talk quickly. But it would be incorrect to write it like that.
beware of students using, and yes, actually writing, shouldn't OF, for shouldn't HAVE. the same goes for wouldn't OF/HAVE. as explained by kitkattail, this is a transliteration of rapid, or "clipped" speech. i came upon this problem as a french teacher while i was teaching hypothetical (if/then) structures. english and french have nearly identical structures with regard to hypothetical senten
written, and spoken slowly, it does have a bit of an odd ring to it. young, inattentive speakers of english are wont to question all sorts of things... at least here in the states.