I find a lot of questions, especially on Stack Overflow, where the question was answered quickly and the solution may have worked for that person, satisfying the accepted answer criteria, but another answer gives a more in-depth and/or correct solution to the problem.
I believe having a small indicator next to the answer, or below the question, would help many people not try the accepted solution, only to keep looking in the thread when it does not work for them.
To quote The Tour exactly,
Accepting doesn't mean it's the best answer, it just means that it worked for the person who asked.