The basic answer is that if a qualifed ob/gyn reviews your medical records and finds that the doctor that delivered your child fell below the standard of care, was negligent, then you do have a good case. Of course as we all know, even good cases, with strong support from medical experts sometimes lose at trial.

The complex answer is that brachial plexus cases come in many different styles. I will try to generally explain:

1. Pre-natal cases: With women diagnosed with gestational diabetes the physician must be concerned about fetal macrosomia (large baby). It is accepted that babies of gestational diabetic mothers are at greater risk for macrosomia, and in turn shoulder dystocia. When reviewing a case, we look to see if in the pre-natal period were there warning signs that should have alerted the ob/gyn that there was a greater risk of shoulder dystocia. In these cases, our position is that the risks should have been explained to the mother and a cesearian section offered. Other pre-natal risk factors that are important include obesity, prior shoulder dystocia, history of traumatic birth.
2. Labor cases: In some instances, there is no indication of gestational diabetes, or fetal macrosomia during the pre natal period, yet during the labor process, there are indications of impending shoulder dystocia. For example, labor is usually seperated into three stages. The first stage is early labor, the second stage begins when the mother starts to push and the third stage is at the actual time of delivery. Depending on some other factors such as how many prior deliveries the mother has had, the second stage of labor should last no more than 2 hours. If it is longer, it may be abrupted labor. Slowed labor can be a sign of impending shoulder dystocia, The labor is slowed because the baby is too big to descend properly. The real problems come though with the use of a vacuum or forceps with a baby with slowed labor that has not properly descended. The FDA has reported increased incidence if injury to the baby when a vacuum is used in the face of shoulder dystocia. Although it is a complex medical issue, if the baby has not properly descended, the doctor should not panic. If the baby's fetal heart monitor is fine, the ob/gyn should leave the baby alone. If it descends, that is fine. If not, a cesearian section can be performed. Using a vacuum or forceps to force a baby with shoulder dystocia down is not correct, and can cause serious injury to the baby.
3. Delivery cases: The third type of case occurs at delivery. In these cases the progress of labor was normal, there is no diagnosis of gestational diabetes and the baby may or may not be macrosomic. In these instances, the shoulder dystocia is first recognized at the time of delivery. Usually when the baby's head shows and then pops back in. This is know as the "turtle sign". At that point the ob/gyn must not panic. If not already done, an episiotomy should be performed, followed by the standard maneuvers to deal with should dystocia-McRoberts manuever, Woods maneuver and suprapubic pressure. If these manueuvers are not done, or if excessive traction is applied to the baby's head during the delivery, it can be the basis of a malpractice case.

These are general descriptions. Before any lawyer can advise you about your case the complete medical records must be reviewed, medical research done, and the lawyer should consult with a qualified medical expert.

(UBPN thanks Ken Levine for contributing this answer.)