Not one of my favorite films, but one that featured Mount Rushmore National Memorial is 2003's "Head of State" starring Chris Rock and Bernie Mac.
Following an unlikely black candidate for president on the campaign trail, the movie opens with some great aerial footage of Mount Rushmore and a singer and dancers in front of the mountain.
More info and the trailer are available at IMDB.com. Rushmore appears at about 1:28 into the trailer. The full movie is currently available on YouTube.