Sometimes the reason they are rescues is because they may be biters. I feel if any dog is biting, the reason needs to be understood -- is it medical or behavioural? Can it be treated? If not, should the dog be put to sleep? Sometimes the latter, the very last choice anyone in rescue wants to take, has to be taken -- sometimes the dogs are clearly just deeply disturbed and unhappy, sometimes they are too unpredictable and could hurt someone. If the dog cannot be kept safely, and cannot be retrained or the medical condition treated, the responsible decision by rescue is to pts. I haven't had to take that decision yet though have had to consider it twice. Rescue is not about happy endings all the time. You have to have the ability to make the tough calls.
I think it is an ethical obligation to determine why a dog is biting because it always indicates some deep level of unhappiness -- most dogs will not bite until they feel they have no other choice. The first thing to do is medically assess. The second is to assess for temperament. If the dog is OK on both, then it is
probably a behaviour issue that can be managed. For me, the borderline temperament dogs are the really difficult ones. Sometimes they can go to where that behaviour can e managed. But who could live with a child being maimed by a biting dog? Most bites requiring medical treatment from dogs are to children (over 70%), mostly by a dog they know, mostly to the face. So there's no way I'd put a questionable dog into a family situation -- has to be an adult home if there's the remotest question about temperament and the need for training.
Rescues are not more likely to bite -- but they are more likely to have behaviour problems. Usually these are owner induced from previous homes -- and the reason the owner gives up the dog is they never trained their dog so they get overwhelmed by the consequences of a hard to manage dog. Usually some basic training will address this type of problem but issues can become very ingrained and rarely, bad enough to lead to fear aggression. Puppy farm/mill dogs can have very serious behaviour and training problems. As noted above sometimes they can be fully addressed, sometimes partially addressed, and sometimes cannot be changed much at all. I think ALL mill dogs need to be medically and behaviourally assessed by professionals, not simply by fostering. I also think any dog showing aggression needs professional assessment before being rehomed. That would be international best rescue practice. I am really lucky that Tara and Lisa of Dog Training Ireland have been willing to give time to do these assessments for me and in some cases take on the questionable fosters themselves for closer assessment and beginning training. Tara has crate and obedience trained a LOT of my more challenging rescues before they went to their new homes as remodelled dogs!
In summary: I'd say that rescue dogs generally are no more inclined to bite than a dog down the street.
Puppy mill rescues fall into a different category from general rescue (eg pound or shelter) dogs because they are generally unsocialised and can have fear aggression problems and there simply MUST be a greater burden on responsible rescue to carefully screen such dogs. Sadly though, this is not done enough which puts such dogs at risk of ending up in the pound or worse when people find they cannot manage the dog and don't feel able to re-contact the rescue about the dog -- as they wrongly feel they have failed. It can put people at risk too from bites, which isn't acceptable -- only an experienced home should take on such dogs with an understanding of how to manage the behaviour and continue to work slowly with the dog.
Ideally, rescues need to give 100% backup to all dogs once they are homed, and give every dog 100% the best chance of succeeding in a new home by having screened and assessed dogs in advance of placing them.