There is no evidence from Joseph Smith's day that he ever said such a thing. The sole source for this claim is one person's journal entry from 1881 that was published in 1892. Joseph Smith died in 1844.
But even if he did think that there were people living on the moon, so what? It was a common belief of the day. There had been a newspaper hoax in Joseph's day in which it was claimed that Sir John Herschel had discovered that the moon was inhabited by people. Further, did any Old or New Testament prophet show a knowledge of science close to that of us today, or a knowledge that would be acceptable to the hard-hearted Bible critics of today? Did any of them grasp the nature of subatomic particles, of relativity, or did they know the value of pi or proper ways to classify birds and mammals?
Does the "moon men" belief make Joseph Smith any less of a prophet than was Joshua, who was fooled by a false report from the Gibeonites in Joshua 9? Was he any less of a prophet than the blind patriarch Isaac, who was fooled by his son Jacob into giving a blessing meant for his brother (Genesis 27:12, 35)? (See also 1 Kings 13 for an example of a prophet being fooled by the lies of others.) Remember, prophets don't speak prophetically in every little thing.
As for the US government being overthrown, according to the thinking of the time, we just had an overthrow of government during the 2010 election. The party in power was "overthrown" and voted out of office.