You already know that they have well-developed personalities, having been around the block or two and know how to interact with people, but is this really a mixed blessing?
The answer (as it is with many things in life) is: It depends.
Older dogs, especially dogs that you acquire from a shelter or other owner, may very well come with a number of pre-existing behaviors. Some of these will be pleasant, while others may require a bit more work on your part to address.
I bring this up, because everyone who adopts a dog should know that there may very well be challenges and its important to acknowledge these before you're surprised. Adopting a dog and then bringing it back to a shelter will only prove to shake it's confidence, which is likely to make it even a less adoptable dog.
The silver lining to this is that you have a chance to help shape your old dog's behavior and use it as a bonding experience.
How can you best deal with these pre-existing behaviors or as I like to collectively call them, baggage?
- Training - Use the opportunity to provide training, whether it be extra time that you put in or go with a professional. I'm not afraid to say that the old adage: "You can't teach a old dog new tricks" is almost always wrong. They might not be jumping through hoops or taking the steps two at a time anymore, but any dog willing to please it's adopted parents are usually trainable.
- Desensitizing the situation - Be careful here. I'm not talking about adding more stress to your old dog's life, but rather, if you can help it, don't avoid stressful encounters. Instead of running in the other direction, reframe the opportunity. Afraid of other dog? Walk near them. Have a strong prey drive? Go to where the critters are and hang out of reach and speak calmly to your pooch (don't pet an agitated dog, it only encourages the agitation.) Acting out and barking to get your attention? Go in another room and ignore it. (This last one I've found particularly useful.)
- Don't put your dog in a bad situation - In some cases, you are going to need to avoid stressful situations. Ever read an ad about an old dog that isn't good with kids or is best as "an only dog"? I see these all the time and would never recommend adopting a dog into environments that already put the dog at a disadvantage.
The important thing to remember is that you're looking for the right dog for you and your family. Understand your strengths, match them with your ideal dog, and be ready to handle the surprises (good and not) that come your way to make life better for all.