As to the question of whether one can actually see Russia from Alaska, Governor Palin was correct: such a view is possible from more than one site in that state. A Slate article on the topic noted that:
In the middle of the Bering Strait are two small, sparsely populated islands: Big Diomede, which sits in Russian territory, and Little Diomede, which is part of the United States. At their closest, these two islands are a little less than two and a half miles apart, which means that, on a clear day, you can definitely see one from the other.
Also, a 1988 New York Times article reported that:
To the Russian mainland from St. Lawrence Island, a bleak ice-bound expanse the size of Long Island out in the middle of the Bering Sea, the distance is 37 miles. From high ground there or from the Air Force facility at Tin City atop Cape Prince of Wales, the westernmost edge of mainland North America, on a clear day you can see Siberia with the naked eye.