Mary Sue: Mary, meet Lazarus Long. He's immortal and can kick your ass and he's got fiery red hair. This is averted in a later Heinlein novel, The Number of the Beast, where both the protagonists and Long's own family find him to be insufferable.
Mary Suetopia: A more downplayed version. Technology has gotten to the point where inhabiting a new planet is as easy as living in a big city, and given that the family did decide to immigrate to the new planet, they do get to settle how they want. It is indeed unrealistically peaceful and efficient, but it did have to take advantage of a whole new planet and technology to make it work.
Unfortunate Implications: Pretty much every woman in the novel (even the one who was a computer when he first met her) considers herself a failure as a woman if she can't bed Lazarus. From an evolutionary standpoint, it could be argued that Lazarus is the fittest male in existence, but women have an almost pathological need to mate with him.