I highly recommend instructors take the time to observe some of their student’s checkrides. Why? Well, remember there are three sides to every story (or checkride). In this case, there is the examiners side of the story, the applicant’s side and what really happened during the checkride. If the instructor is there to observe, he/she can really learn the truth by seeing what actually took place.
The instructor will learn several things from observing. He can learn how the examiner conducts the ride, everything from the examiners personality, how questions are asked to the flow of the ride.
The instructor will be able to observe his students performance. The instructor will be able to see any weak areas and address them with other students.
I can tell you from previous experience, observing a student’s checkride is nerve racking. You know you've covered the material and the student knew it when you signed him off, but for some reason, now he can't even recall his own name. That's the result of stress and it's usually caused by the fear of the unknown. What you learn from observing previous checkrides, you can share with your current and future students. Hopefully, this will lower their stress level and allow them to perform better. Incidentally, instructors who have observed previous checkrides have a higher pass rate!
Just so you know (and to keep other DPEs and the FAA happy), my checkrides do change from applicant to applicant in accordance with the PTS. What that means is the PTS describes what I test but not how. For example, some questions might be asked differently or I might ask the applicant to divert to a different airport.
So, if you have a student taking a checkride with me, you are welcome to sit in and observe.