Cathy walks in during the kitchen scene where Patty is explaining puppy love to Richard. She first walks right-to-left with her double's facial profile exposed. She then returns walking left-to-right with her double's full face exposed, clearly showing it is not Patty Duke.
When the exterior of the hospital is shown during the time Patty is admitted, tall palm trees are seen. The hospital is suppose to be in a New York City borough - a framed wall diploma in the doctor's office says: New York University. Season three was filmed in California, hence the west coast exterior location footage.