I ride an OTTB broodmare who is an angel - and this qualification comes from me, a very nervous middle-aged novice. She is just perfect. Fit and willing, no spooks, bucking, sudden moves, ear-pinning - nothing but responsive and comfortable riding.
The only thing that she did wrong sounds rather dangerous but it wasn't actually: she reared in hand when she saw a foal. But she did it vary carefully, low and away from the handler and out of pure excitement. We are putting it down to her pregnancy hormones as she was bought pregnant and still is.