What general observations about life or human nature does the author make or imply? Do the characters make any such observations?

Unlike most writers during the Elizabethan era, Shakespeare refused to focus on politics and religion in his writing.  He and his characters achieve a universality this way, as they are not mouthpieces for polemic diatribe.  He honors the Greeks, Romans, Judeo-Christians, and the secular.  In this way, he is a humanist ahead of his time.  Shakespeare somehow found a way to synthesize and honor all belief systems without alienating any.

Also, Shakespeare focuses on the eternity of art and love.  Although I would not classify him as a Romantic, he did exhibit a idealism when it comes to love at all costs.  Many of his characters demand true love, and are willing to suffer greatly if they do not get it.  Whether it is Romeo and Juliet or Desdemona, Shakespeare's characters refuse to settle for lukewarm affection; instead, they demand, and are prepared to die for, passionate love.

In short, Shakespeare has the biggest heart, I think, because he worked in a collaborative industry--the theater.  He surrounded himself with open-minded people of all classes.  He did not publish his work during his lifetime; in this way, he guarded himself against artistic pitfalls of self-righteousness, hubris, and petty grievances.