No. He didn't make a mistake. The doctrine that these sealings were supposed establish was correct and is still the same doctrine. The implementation needed some work. You have to remember that we didn't get perfect knowledge from the beginning. We had the doctrine, but not all the information about how to implement the doctrine.
Are you sure that Joseph Smith implemented the "law of adoption"? I do not know who coined the phrase, "law of adoption" but when Joseph Smith first implemented the sealing ordinances, he included family members and friends, binding all relationships and making new relationships, family members that weren't biologically connected. It seems logical that if you could adopt a child legally then one should expect that the child would be sealed to you. It's not a far stretch for members who were eager to associate themselves with the prophet or apostles would seek to be adopted into their family. The same thing happened in the Philippines during the Spanish occupation. Filipinos didn't have last names and so, the Spanish government called for the people to choose a last name. He intended to have them associate with each other so family connections could be established, but that's not what they did. They all started choosing the name of a Catholic saint as their last name, even within the same household. It is not uncommon for people to want to associate with an authority figure who will get them closer to their goal.
You probably know that our practices are still going through changes. It wasn't uncommon just 15 years ago for members to do work for dead celebrities or holocaust victims even though there was no family relationship. This created a problem for the church and they've taken steps to prevent that from happening again. The doctrine has not changed. We are still forming one human family being sealed from Adam to the last man. And you know what? We still seal adopted children to the parents who adopted them.
Well, sadly, you're more wrong than ever.