The plaque at Lake Archimedes honors R. Petrovicz, Ssgt (Ret) US Army, 1965 - 2011. This is a tribute to Robert Petrovicz who served as Eureka's producer from 2006 to 2010.
Spaghettification is an actual scientific term for what happens to an object when it gets pulled into a singularity.
The insignia for a "captain" in the navy is an eagle which is the rank insignia of a full bird colonel in the army air force and marines. A navy captain, army colonel, air force colonel and marine colonel are all the same grade, O-6.
Monroe's rank on the ship is Captain, and she wears the uniform rank insignia of an eagle, the same as a colonel in the Army, Air Force and Marines, which is the same grade as a Navy and Coast Guard Captain. (However, the officer in charge of a vessel is the Captain, regardless of their actual rank.)
one of the people going on the ship to titan is named Yamamoto. This could be a reference to the Macross Saga or Space Fortress Yamamoto which are both famous Anime about giant space travelling ships. It could also reference Isoroku Yamamoto, the architect of the pearl harbor attack by the Japanese during WWII>