[Minor spoilers ahead]
Lesson 1: It is good to be both hard-hitting and compassionate. What I find most intriguing about the key scene of the movie is that at that moment, Frost was both hard-hitting (otherwise he would not have gotten any results) and compassionate (otherwise, Nixon would not have opened up as much as he did).
Lesson 2: Admitting a mistake can be positive for all involved parties. According to Berardinelli, the aftermath of the interview was positive for both Nixon and Frost (and the American people, I suppose):
For Frost, it assured him of a long and prosperous lifestyle and recognition as more than a talk show host. For Nixon, ironically, it was not the end. The admission allowed him to move beyond Watergate and, despite the film's assertion to the contrary, he achieved a degree of rehabilitation in the public eye. Presidents Reagan, Bush (Sr.), and Clinton all turned to him for advice and, at the time of his death, far more was said about his positive legacy as a foreign policy guru than about Watergate. Nixon will always be linked inextricably with Watergate, but the Frost interviews allowed him to enter a new phase of life.