Question: I know some skills are best learned while a person is very young, like a second language, or absolute pitch. What are some other skills that are best learned while young and can be beneficial to a person? My thinking is that since those skills can only be learned while young, then that would be the time to focus and teach them. Other skills like reading/math can be focused on later.

Answer: 
Beside language and musical skills, one thing that is never thought in schools is *character* or *assertiveness* skills, they present a challenge as sometimes the parents don't posses them, although there are many good books on the topic (just check an online book store and read the ratings!). *Meta* self-help books such as the *7 habits of highly successful people*, which go beyond mere tips to forge true character are recommended.
Kindness, following directions (need for school and business, not just discipline), sharing, group 'work', sportsmanship, kindness (o-did I already say this), empathy, creative play (work), kindness (o-did I say this again), problem solving skills, how to deal with difficult people, kindness (again).

I can give suggestions on how to teach some of these if you wish, but the question was what skills should be taught. It is very hard to get rid of bad habits if these skills are not taught from the beginning.