Are there any important issues that Whitman speaks to in "Song of Myself" that must be taken into consideration no matter the century?

I would say that the contemplation of life and death is a timless topic.  When the child asks, "What is the grass?"  the speaker takes the child seriously and contemplates the role of the ordinary in our lives.  Upon consideration, he muses that everything that lives has significance, that one blade of grass is the seedling for the next, and that therefore we are all a part of the enormous, cyclical nature of life and death.  If we view ourselves as a part of an ongoing circle, there really is no death. 

Here is an excerpt from Section 7 that encapsulates the speaker's view of the interconnectedness of life and death:

I pass death with the dying, and birth with the new-wash'd babe, and
         am not contain'd between my hat and boots;
   And peruse manifold objects, no two alike, and every one good;
   The earth good, and the stars good, and their adjuncts all good.

   I am not an earth, nor an adjunct of an earth;
   I am the mate and companion of people, all just as immortal and
         fathomless as myself;
   (They do not know how immortal, but I know.)