My parents allowed me as a teen to adopt an older dog (long-haired dachshund). Cutest little guy. Unfortunately, we soon discovered that the dog was dying of some incurable disease and the original family didn’t want to deal with watching him die. So, it was a sad and deceitful situation.
Having worked as a dog walker a few years ago, I dealt with a few older adopted dogs with health issues. The individuals who adopted them knew in advance and were prepared to deal with potential crisis situations.
The only cons, I would say, would be not knowing of any health or behavioral issues in advance of adoption. Otherwise, knowing what you’re getting into, no matter how old or in what health condition, would be your personal choice as opposed to being a “con.” Some people enjoy caring for older and/or ill dogs.