In the opening narration, the narrator states that the crew of this space ship is far from Earth in "a far corner of the universe". Later, one of the characters mentions that they're "655 million miles from Earth". 655 million miles would put them somewhere between Jupiter and Saturn. What's more, when they look up at the sky, they see two suns.
As Peter goes to speak to the fisherman, the shot of the two on the bridge is obviously a photograph.
Almost all of the "frozen" people can be spotted moving in their scenes. This is most notable in the campaign speech scene where several of the actors can be seen blinking their eyes. The pageant contestants also are slowly swaying back and forth.
When Captain Webber is speaking to Mr. Wickwire, he made a reference to "Meteorite Storm". He should have said "Meteor Storm" because meteors become meteorites only after they pass through the Earth's atmosphere and hit the ground.