What are some modern elements in Ibsen's play A Doll's House?

There are a number of modern elements in Ibsen's A Doll's House, which make this play timeless.

Perhaps the most notable element is that of equality of the sexes.

In the nineteenth century, women's lives were limited to socially prescribed behaviors [...] [T]he controversy surrounding sexual equality [is] an important part of the play.

The double standards of the past still exist today. Though not as prevalent as was the case in the nineteenth century (the setting of the play), and even in light of laws that have been passed to attempt to guarantee equal pay for equal work regardless of gender, there is still difficulty in many areas for women trying to break through into professions traditionally dominated by men and be paid commensurate with their training and experience.

This could also be said regarding class. Torvald considers Krogstad contemptible and beneath him because Krogstad made one bad choice and went to jail—even though they went to school together. We can infer that Torvald's contempt is also based upon his perception of Krogstad's weakness. Torvald is dismissive of Christine Linde as socially inadequate because of her financial standing and her need to work. From a modern vantage point, there still remain obvious divisions—and barriers—between social classes in the United States based upon wealth, education, social standing, ethnicity, race, gender, etc.

Another element from the play that speaks to a modern audience is that of "identity and search for self." When Nora realizes that her marriage has been a sham and her husband has no regard for her as a person—as an equal—she understands that she is incomplete and must find out who she is: not based upon her husband's or society's expectations, but upon her own perceptions of what she learns as she makes her way out in the world. 

HELMER: But this is disgraceful. Is this the way you neglect your most sacred duties?

NORA: What do you consider is my most sacred duty?

HELMER: Do I have to tell you that? Isn't it your duty to your husband and children?

NORA: I have another duty, just as sacred.

HELMER: You can't have. What duty do you mean?

NORA: My duty to myself.

Nora also announces:

I can't be satisfied any longer with what most people say, and with what's in books. I must think things out for myself and try to understand them.

Other elements of the play that have a modern relevance are betrayal and deception. We can find these elements with regard to many areas of society: divorce; fraud (e.g., Ponzi schemes); abuse of women, children, the elderly, etc.; and, drug wars and terrorism, to name a few. All of these difficulties are the result of deception and betrayal.

While Nora deceives her husband (and Krogstad) to save Torvald's life, Torvald deceives Nora in telling her that he loves and wants to protect her. In truth, he enjoys possessing her as an object, something he owns. And when he is afraid his reputation will be ruined by scandal over Nora's fraudulent loan, his only desire is to protect himself.

Torvald likely sees Nora's crime as an act of betrayal; and he is completely oblivious to the fact that she prevented his death. His betrayal of Nora is more stinging. Torvald does not respect Nora as a person; he treats her like a possession; he turns on her when his reputation is at stake; and, he threatens to take their children out of Nora's care—the ultimate betrayal from Nora's position. He values society's belief that he is honorable more than anything, which is another betrayal.

HELMER: I would gladly work night and day for you. Nora—bear sorrow and want for your sake. But no man would sacrifice his honor for the one he loves.

NORA: It is a thing hundreds of thousands of women have done.

Ibsen's A Doll's House is full of themes that speak to a modern audience.