Some have problems while others do not. Our Rescue Groups insurance precludes accepting dogs with a history of vicious behavior so we seldom have biting problems - except for moms with newly born puppies who are sometimes quite ferocious in defending them.
Since we are often the first people who have offered these dogs love, they will often bond to us and not want to share us with other dogs. We just are kind to them but, do not let them get way with growling at dogs who come near us.
With some dogs, it takes a while before they become relaxed in our home. Our goldendoodle, Holly, acts like a therapy dog for scared rescues. It usually takes Holly just a day or two before the rescues are sleeping with her.
House training is another problem with some rescue dogs but, all our floors are tile and we have a large back yard that the dogs make use of. The other dogs seem like they help train the dogs who have not quite mastered where to go potty. However, we don't think that you can house train a dog unless that dog is living in the house. So we don't keep the dogs in kennels and definitely don't keep them in the yard for long periods. We are fortunate in that we have a very large home.
Some rescue dogs are very frightened of people but, we can usually get around that type of behavior with low key love and affection.
I really give a lot of credit to our own four dogs who are confident enough of our love that they don't need to compete with the rescues.
It often takes two weeks or more for a rescue to begin to feel comfortable in a new home. We can see the changes as they begin to play with toys and otherwise act as normal dogs.
Occasionally, we need to make use of professional training as we did with Pepsi and Cola who were rescued from beneath 14 lanes of Los Angeles Freeway traffic in a storm drain which they were living. Pepsi was the defender of his sister, Cola and Cola was the shrinking violet, scared of everything and everybody. On the advice of a professional trainer, we adopted these two dogs into different homes where they are living happy and normal lives.
When we get dogs who are very frightened of people, we have a foster family who specializes in caring for dogs like this and turning them into well adjusted dogs and puppies. Our foster has two precocious young daughters who don't let the feet of a puppy hit the ground. They carry them around almost 24/7 and sleep with them. This does wonders for shy dogs.
All in all, we treat each dog individually and I am happy to say that we have had no failures. There is a home for every dog. We just need to help them find that home and help them get ready for it.
Lots of work but really worthwhile...