I think you have to look at what they don't mention, rather than what they do.
For instance, the horse in the advert, clearly only mentioned an experienced rider and dressage. Therefore indicating that anything else was an issue.
I think if I was looking for a horse now, I would want to see in an advert good to load, shoe, box. Goes first or last hacking and fun rides, hunted and goes front or back. Doesn't kick, buck or rear.
And if you want to do shows, I would expect to see that mentioned too, and not just one or two shows. And to mention what it has done in shows. I wouldnt however expect to pay under £3-4k for it, and wouldn't really look at anything under 6/7 years old. Up to 12 years old, more depending on experience, and then would look at a bit of a sliding scale downwards.
I would be wary of anything 5 years old who has done all of the above, it has probably blown its brains or it is about to hit the kevin years.
Very difficult, buying horses - and you only learn from your own mistakes which I did!
Also, I think you need to understand how often horses are ridden. My own horse is very good indeed during the summer - he is ridden much more, and is turned out 24/7. During the winter he can be an absolute nightmare - he gets extremely low value feed and I will not feed haylage. But he is ridden less because I work full time, and the winter is tricky for us. So that is a question I would definitely ask of any buyer, and would beware of how fit they look during the winter months.
My YO's daughter had a very short pintaloosa on loan. She was guaranteed 2 years, but 8 months into the loan the owner wants to sell it. It is 13.2, YO's daughter is little and is 26. She has worked in yards and ridden show jumpers. Pony is apparantly worth 3k on Pony Clubs DC's reckoning. Actually it isn't. It went to Pontispool ONCE with YO's daugher and was incredibly badly behaved. A child would have no chance of controlling it. But it has been to Pontispool. It hunted ONCE, but has hunted. It has been on ONE fun ride, but has been on Fun Rides.
So I think the quantity of what it has done is a massive indication.