Generally the appellate court's review lower court decisions under a very difficult standard-and will reverse if it finds "abuse of discretion". Wide latitude is given to Judges so it is difficult to win on appeal. A very good record of all the proceedings must be made and you should request specific findings of fact if you have serious hopes of being successful on appeal. Within 10 days of the final order, you can file a Motion for Reconsideration and provide the Court with "new facts" and evidence that was not considered. You should also request an "evidentiary hearing" and have the custody evaluator take the stand to testify about the reasons and grounds for the recommendation that father have custody. Walking the Judge through the reasons set forth in the custody evaluation may be a persuasive tool in getting the Judge to see the harm the child is exposed to during mother's care.
Did your son have a lawyer at the trial? If not, the chance of his bringing a successful appeal goes from small to VERY small. Appeals are expensive, take time, and most are not successful. Your son needs to sit down with an experienced California family law attorney and review ALL the facts of his case, and his options.