For me success is defined not only in whether or not the dog can execute this or that behavior. You can create some pretty compliant well-behaved dogs just by shutting them down. But just precise behavior on cue to me is not the whole picture of successfully working with and training a dog.
Rather than discreet behaviors, I'm more interested in a dog who really knows how to learn, and if a trainer can demonstrate for me that he or she understands how to do that, I'm all ears/eyes. When it comes to whatever demo dog they have, I want to see a happy, operant, experimenting, exuberant dog (appropriate to breed temperament of course) who can learn a new behavior quickly and cleanly, because that is a dog who knows how to learn. I've never done it because I've used the same training center for all the classes I've taken, but I might ask the trainer to get their demo dog and start to teach some silly random new trick to see how they worked together, what the dog and trainer's attitudes were and how quickly and cleanly the dog was learning. I don't think a dog who can run through a set list of behaviors is going to give me the whole picture because I want to see how that dog learns in the moment, not just doing something that's already been rehearsed a million times and was trained who-knows-how.
My own trainer does one thing that I absolutely loathe and refuse to do because it just smacks of learned helplessness and seems to fly in the face of everything else she teaches. I'm working on getting the same result through different means. The fact that she can get a small dog or puppy to lay down and stay down by stepping on the leash near the collar does not impress me (and Marlowe won't stand for that anyway). Instead, I'm shaping the same behavior (it's supposed to be an "off switch" for the dog, which I understand the value of, but I completely hate how she teaches it)--lay down and put your head on your paws and don't look at me because we are not working right now. It's taking some time (mainly because it's not a huge high priority for me) but forcing a dog into a position and teaching it that resistance is futile is not successfully teaching that dog anything.