We almost saw everything.
According to producer Steven Moffatt, a scene depicting Kingston in the buff, winking at someone off-camera, ended up on the cutting-room floor. "Deleted, yes," he replied when asked about it on Twitter. "Too naughty, don’t know what I was thinking.”
The scene was supposed to be part of the episode "The Impossible Astronaut." So was a scene involving Nazis looking for the doctor. Both were part of the first Series 6 season trailer but never saw the light of broadcast.
And don't look for them as "deleted scenes" in the Sixth Series Box Set, either.
Apparently, some things that happen in the Tardis stay in the Tardis.
More details from The Eleventh Doctor Volume 3, according to our friends at Dr. Who TV:
The readthrough script for [The Impossible Astronaut] had I minimal changes before issue as shooting script. The main alteration was the ultimately deleted scene at Stormcage where the governor remonstrated with River Song over her previous 15 escapes under his predecessor, “Oh, it was never fifteen – unless you’re counting holidays and hair appointments…” said River as she opened a cupboard on the cell wall and pulled out an impossibly long clothes rail of dresses commenting, “Don’t mind my wardrobe. Teensy bit bigger on the inside!”
There were more changes later made to [Day of the Moon]; the opening sequence with Rory and Canton was set in Chicago’s waterfront docklands and the final scene with the little girl was set in New York. The Doctor and his friends had been gathering information over two rather than three months between instalments. Still to be added were the Doctor’s comparisons of the Silents to the Roman Empire, the Doctor describing the sensation of the Silents being around, and much of a sub-plot about the Doctor’s beard.