Point of croup is too far back and exaggerated, weak hind end overall, long cannons behind, upright shoulder, upright pasterns.
I do think she carries her neck well and probably hasn't been ridden in any headsetting device (considering her natural throatlatch, etc, I would say she is naturally behind the bit), she just doesn't have the hind end to carry, and her legs don't suggest much better. I would say low level dressage, low level hunters at best for her. The only thing I wouldn't fault is the riding, the rider presents her well and her basic training looks to be good.
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I can see what you mean on a lot of those points, and on a closer look I'd add that her front pasterns seem overly long as well. However, if she carries her head & neck naturally like she has it in the photo with the rider, breaking at the third vertebrae instead of the poll, I would find it hugely detracting. That's the thing I dislike about her the most
I didn't realize there was a video until I went back to the ad just now; I can't say I'm terribly impressed by the rider, but would agree that the horse seems to have good basic training.