I'm not even going to comment on the jumping picture.There is a lot wrong, and IMO its not fair to critique the horse. She's doing what she can based on the rider.
Besides needing topline, she doesn't look too bad, though I'd want to see better/more pictures of her and from different angles too.
I would be curious to know what exactly her issues are with trailering and grooming. If you're wanting to compete or trail ride or anything, the trailering issue could get in your way (I know because I have a horse who has trailering issues and its messing up what plans I had for him). And the grooming issues should be interesting. She looks nice and shiny in the one picture and looks well groomed, so i'd just be curious what those problems are.