As a writer, these twin goals pose a problem: How to set the record straight without bogging down the story?
The answer is simple (even if the execution is not): Keep the reader in mind at all times. When correcting mistaken notions about my main subject, I do so mostly by simply giving my version, and leave the arguing to the endnotes. Don't weigh down the narrative with pedantry! But sometimes there are misapprehensions that shape our understanding of the central figure—stories so iconic that they must be addressed explicitly.
With Commodore Vanderbilt, this came up a number of times. One of them involved his relationship with Victoria Woodhull and her sister, Tennessee Claflin. Their friendship has been blown wildly out of proportion; most writers accept without question the idea that Vanderbilt wanted to marry Claflin and funded their brokerage house, purportedly the first woman-run brokerage on Wall Street. When I shot down such notions, I had to do so directly. In special cases like this, I think a discussion of the evidence actually serves the reader, for such tales go to the heart of the public's notion of Vanderbilt. In most instances, however, it's best to let the correct version flow without any fanfare.
Then there's the matter of correcting the historical record when it comes to larger issues. When I put my subjects in context, I try to avoid taking for granted the standard version of that context. I try to ask hard questions about American history, as illuminated by my main character. In Jesse James, I tackled the historiography surrounding Missouri's internal divisions in the Civil War and Reconstruction. In The First Tycoon, I offered a new interpretation (well, not entirely new, but with my own twist) of the antebellum Democratic and Whig parties, particularly with regard to their positions on the economy. I argue, for example, that Jacksonian Democrats favored the market economy, but were disturbed by the abstract nature of corporations, paper money, and securities. I also identify a deep suspicion of competition among many Whigs, which helps explain the origins of the "robber baron" label, first applied to Vanderbilt.
Again, there are key moments when it is worth interrupting the story to examine these questions. But such discussions must contribute to the story. It's my job to convince the reader that she or he needs to grasp what I'm explaining in order to follow what happens next.
And that is the ultimate law that a writer should follow at all times: Give the reader a reason to turn the page. Always.