Which white spots in which photographs, specifically?
I see a lot of transmission noise in the earlier pictures, especially Luna-3. Transmission was entirely analog in those days, and the artifacts depend on the transmission speed and modulation type.
Digital image transmission with error correction didn't really get going in the civilian space programs until the mid 1970s, e.g. with Viking on Mars. Even Lunar Orbiter's high quality images were transmitted as analog FM signals; the receiver tapes (made with modified professional video recorders) were dusted off and digitized some years ago with outstanding results. See the Lunar Orbiter Image Recovery Project (LOIRP).