A good question. You are correct that the tone shifts at times. In the preface, for example, there is more of a direct appeal, almost as if Twain were marketing his book to potential readers. After that, the approach shifts. However, a few qualities run through the book, and so I'd say the tone is one of affectionate distance, which could also be called gentle irony. Take a look at this early passage:
"The old lady pulled her spectacles down and looked over them about the room; then she put them up and looked out under them. She seldom or never looked through them for so small a thing as a boy; they were her state pair, the pride of her heart, and were built for “style,” not service—she could have seen through a pair of stove-lids just as well."
The level of detail shows affection, as does the "pride of her heart" line, but Twain is gently mocking the woman, and through her, all people.