@Ylvamoon is right - any rescue dog will come with their own baggage. We have had two rescue dogs - one from the Dogs' Trust, and the other from Rehoming Cyprus Pointers, and both have had issues - mainly some nervousness and clinginess - but both the Dogs' Trust and the Cyprus rescue were very diligent in ensuring that we were well aware of the potential problems.
As I said in my first post, we had a home check visit from a representative of the Cyprus pointer rescue, and if we had had any serious problems, we could have contacted her for advice in person, or got back in touch with the lady in Cyprus via zoom.
Maybe we have been lucky both times, but both times we ended up with loving, friendly, obedient dogs, who fitted seamlessly into the family, and who were/are delights to own.
Our first rescue dog was listed on the Dogs' Trust as a labrador cross, but looking at her, it was crystal clear she was a pointer cross, with pointer dominant, and when we lost her (to progressive, untreatable anaemia), we were sure we wanted another rescue pointer/pointer cross.
We ended up going to the Cypriot rescue because every single dog we considered, from UK rescues (mainly the Dogs' Trust and SSPCA) couldn't live with cats, and we have a cat. He is a bit of a bastard (hence the nickname CatBastard) but he was here before the dogs, so does deserve consideration. The rescue on Cyprus was willing to get our current rescue pointer cross together with cats, and see how she responded.