Yesterday’s Boston Globe had an amusing op-ed in which Alan Cox and Stacy Keach (the Frost and Nixon, respectively, of the touring production of Peter Morgan’s play) and Bob Zelnick, the gray eminence of David Frost’s researching team, discussed the play and its connection to the historical record.
Those who have seen the touring production will have noted that Keach’s compact face does not resemble RN’s and that he compensates for this, and for the dissimilarity between his vocal timbre and the president’s, by meticulously reproducing Nixon’s speech patterns in a way that Frank Langella does not. But Keach explains that at the start, his plans were different:

At first, I decided I was going to do everything possible to emulate Nixon to every detail. I had contact lenses made, I had a nose made, I had a chin made. I even had eyebrows made. I had teeth made. And I threw it all out except for the hairpiece, because I looked at the photograph of me in that position and I showed it to my wife. And she said, “You don’t look anything like Richard Nixon. You look more like a Chicago gangster.”

And Zelnick brings up the subject of that drunken midnight phone call by RN to David Frost, so central to the play and film, that never happened in real life:

One expects approximation to the truth in areas where there may not be a complete record. There was enough drama in the Nixon presidency so that you didn’t need a midnight phone call to establish the character or the events.

And Alan Cox explains part of the appeal of the play and film:

Q: Why do you think there has been such a great response to “Frost/Nixon”? There’s such an appetite for it, when “W.” really didn’t get such a great response?

COX: ’70s clothes.

Indeed, Oliver Stone’s film Nixon, which underperformed at the box office, was skimpy on the bell-bottoms. But then again the 1998 film Dick had bell-bottoms galore and its ticket sales were minimal.

Keach and Cox also tell what happened when the (George H.W.) Bushes attended a performance in Houston. It’s all quite worth reading.