Ddog2, who is currently curled up on the couch between dh and me, came from the Dogs' Trust, and had been in kennels there for a month or more.
She settled down pretty quickly at home - she had previously been house trained, and hadn't forgotten that, and seemed pretty relaxed here from the word go.
That said, she does have her issues. She is very attached to dh - he is her special person - and she wants to be in contact with a person - preferably dh, but I will do, for a lot of the day (and night - she sneaks upstairs and opens the bedroom door to get on the bed between us! We can leave her at home alone (well, with ddog1 and CatBastard), and she will just settle down and sleep - we've never had any issues with her wrecking the house if she's left at home.
We don't know how many of her issues are down to the time in kennels, and how many are due to her previous history - she had a couple of litters, was handed on to another wonder who lived in a city flat, which wasn't suitable for her, as she is a big dog, and was then given up to the Dogs' Trust - after all that, we think she is entitled to the odd quirk.
I assume that any reputable rescue would assess their dogs and would be able to tell you any major issues, and would make sure that the dog was the right dog for you and vice versa, and would offer support post adoption.
For all her quirks, ddog2 is a perfect fit for us, and is a much loved member of the family. I can't recommend the Dogs' Trust highly enough - they were great with us.