The concept of exceptional inheritance is certainly a prevalent theme in A Doll's House.
Nora's character is said to have inherited her father's suspicious ways and looseness with money. Her father's reputation was not "above suspicion" and clearly her own secretive machinations suggest a tendency to clandestine behavior. Sneaking macaroons, taking out and paying off a secret loan to Krogstad, and attempting to hide the existence of a letter from Krogstad are all examples of Nora's secretive antics. When it comes to money, Helmer direclty connects Nora's impulsiveness to her father.
Additionally, Nora worries that her children will be "poisoned" by her crime (forgery) when Mrs. Linde suggests that any household containing a criminal will ruin its children. This is in keeping with the notion of inheritance.
Dr. Rank claims that he inherited a spine disease from his father which leads to a diagnosis of certain death while Rank is still near the prime of his life.
Krogstad is set on maintaining his position at the bank because he feels that it is his only path to rehabilitating his reputation. If he cannot regain his honor before his children come of age, they will inherit his bad name and suffer through a life of no oppotunities for advancement or success.
These examples clearly show that extraordinary inheritance is a theme in A Doll's House, however we should analyze the ultimate impact of inheritance on the characters' lives before concluding.
For Nora and Krogstad, the idea of passing on dishonor to their children is avoided through positive action. Nora decides to become her own person, eschewing any significant connection to her father and Torvald.
Krogstad avoids the fate of inheritance as well as a result of his marriage to Mrs. Linde.
Dr. Rank does not escape his inheritance, but we can say that he failed to take action to avoid his fate. He did not enjoy himself, as his father had done in his lifetime, until the very end. He did not confess his love for Nora until it was too late. He acquiesed to what he saw as his fate and so "chose" his inheritance.
One interpretation of the theme of inheritance then is to see it as a suggestion that circusmstances do shape a person's behavior but do not determine a person's fate. One can choose one's own fate, regardless of parentage and regardless of circumstance.