It's an interesting question, although I don't think I'd call this "customer service." That sort of makes it sound like the alliance is an entity somehow separate from its members, or that at least some members are basically there to "receive" from the alliance, whereas my view of an alliance is one in which each player contributes according to his or her abilities and interests and the alliance's need.
I think a lot about how my alliance can add value to its members. Of course the friendship and encouragement is a really big part of it, and material support with resources can help, not to mention mutual defense. I think alliances can add value by disseminating information and education to members, such as by mailing updates on tournaments and other server activities as well as new releases. Some alliances have extensive forums (either in-game or separately) with massive amounts of information, calculators and so on.
Balancing the needs of basic education for new players and more nuanced and detailed discussions among more advanced members is also a challenge. As an alliance leader who is still a relatively small player, I rely on the veteran players in my alliance to feed and dialogue with each other, although I think questions from newer players can also stimulate more veteran players to try new things or re-test old understandings.
I'm interested to hear how others handle such things or see their alliances handling such things, what you like and what you don't like, what you'd like to see more of.