The idea of having a personal "mission" can be appealing. However, for myself, I find it somewhat misleading, and I'd like to explore why.
Rand's characters all had missions, and they knew what those missions were early in life (as Rand claims she did). Roark knew he wanted to be an architect at age 11, and so on. Of course, not everyone knows what their (professional) mission is in life at age 11, and a young Objectivist could feel guilty for not having that kind of focus (I know I did). It can take a long time to discover what one is good at, and in my case I did not stumble onto my profession (designing internet applications) until in my late twenties, when the technology for my profession finally reached a fairly high level of maturity. With the pace at which technology changes these days, it's possible that my ideal professional mission actually involves a technology that hasn't even been invented yet. The idea that I could (or, Rand forbid, "should") know about a mission before the enabling technologies have been developed seems to speak against the idea of a stable mission that one can discover early in life. I think that in the last few decades it has become more and more important to retain some flexibility with regard to one's professional mission. Perhaps this issue could be addressed through levels of abstraction (my mission is not be a great COBOL programmer, but to be a great programmer), but I'm not sure.
What I'm even less sure about is the ultimate value of having one over-arching mission in life. I see my own mission as seeking personal fulfillment as the best human being I can be. What that entails professionally or personally I have a hard time putting under the rubric of one mission. I feel this is especially difficult for me because I have many talents in which I find fulfillment -- in my case, music, poetry, philosophy, business, computing, and even non-professional aspects of life such as friendship and spiritual development. It seems that choosing one mission might force me to choose between the different things I find fulfilling. Note in this connection that none of Rand's heroes had hobbies -- their focus on their mission was single-minded. You didn't see Rearden writing poetry or playing the piano or whatever in his spare time -- he had no spare time because he was so focused on his mission. And Roark's room at the Keating's house in college is described as containing only his architectural drawings and some clothes: no books, no music, no posters, no "human touch". Roark was a monk whose religion was architecture -- and that religion brooked no false idols, allowed no competing (or even complementary) gods, and demanded total devotion.
I find this unhealthy. Personally, my mission in life is fairly eclectic. The great French composer Saint-Saens once said of his own variety of interests that it "is perhaps a great defect, but it is impossible for me to correct it ... one cannot alter one's nature" -- this from a man for whom composing music came as easily "as an apple tree producing apples", yet who insisted on writing plays and poems, conducting research into astronomy and acoustics, and publishing articles on history and philosophy. How unfocused, how un-Randian, how untrue to his "objectively correct" mission -- yet how fulfilling for him as an individual!
To my mind there is more than a whiff of deontology in the thoughts of those who advocate the mission idea. David Norton, for all the value of his book "Personal Destinies", often speaks as if one has an obligation to fulfill one's mission, not for the sake of one's happiness but just for the sake of fulfilling one's mission (or for the sake of one's "daimon"). And Norton is a fairly individualistic advocate of personal misssions -- don't get me started on someone like Stephen R. Covey (of "Seven Habits" fame), whose justification for pursuing one's personal mission is service to others.
Also, it's not clear what a personal mission really is. Some have construed personal missions as goals, others as values, others as plans. I think all high-achieving people have strong values, plan for the future, and set goals regarding the projects they want to complete in their short span on earth. To my mind, this is different from having one over-arching mission in life. I am full of ideas and plans for projects, I pursue them with gusto, and I guess you could say that these things comprise goals I have for my life. But I don't feel that there's one mission that embraces all these aspects of my life. The hard part, to me, is understanding exactly how goals, projects, values, relationships, and so on come together to form a flourishing life. Although I think that philosophy has much to teach us here, I don't think anyone has the answer to that question because the answer comes from living and reflecting on experience. Much of the answer is practical and particular, specific to my context -- and my own experience tells me that defining a personal mission is not the answer, either. The closest I've come to defining a personal mission is the front door to my website, but even this is fairly abstract and diverse (dare I even say "eclectic"?) -- which is not a monolithic mission but more of a credo.