How many women have side effects from oxytocin in labor?

All of them: Oxytocin typically increases contractions and that typically causes increased discomfort, so in that sense all women have a side effect. In addition (and I am really not trying to be a wise guy) since oxytocin is the drug at the center of more malpractice litigation than any other drug you should speak with your practitioner. It is a very important and useful drug that deserves discussion.

Extremely rare: Obstetericians are generally very skilled in using oxytocin, and its effects are very closely monitored in labor. In competent hands, it has been an effective and safe med for almost 60 years -- but overly augmenting labor contractions without a ripe cervix can result in failed deliveries, c-sections, and worse.