The ship shown has hull number 115 which is the USS Mobile that was an amphibious cargo ship used in Vietnam. It was decommissioned in 1994.
The aliens ask if their "experiment" has failed which would seem to imply that Bill and Ralph are the first ones paired. In Operation Spoilsport (1981) they find out about another pair from many years ago which would imply the experiment the aliens are actually talking about is the Ralph and Bill pair.
When Ralph enters the ship to fix the hole in the side, a front shot shows Ralph's hair as very wet, but when you see the rear view of Ralph, his hair is completely dry.
The destroyed planet that the aliens show to Ralph and Bill is Mars. This should be obvious when they fly over Olympus Mons, the largest and most recognizable volcano on the planet.