Claire Forlani was cast as Trillian St. James. She even started shooting, but walked out after just three days, due to creative differences with director Stephen Sommers. The part subsequently went to Famke Janssen.
Famke Janssen's character Trillian is named after the Hitch-Hiker's Guide to the Galaxy character of the same name. Although here Trillian is her actual name, in Hitch-Hiker's it's short for Tricia McMillan.
The "Chinese M1 L1 triple-pulse assault rifles" used by the pirates are actually heavily modified Calico M-960 submachine guns fitted with 100-round magazines (as opposed to the "thousand-round capacity" mentioned by Hanover). Five non-functional rotating barrels were built around the actual barrel of each Calico and driven by a small electric motor connected to the trigger, so that whenever the gun was fired, it appeared to be firing out of the rotating barrels.
In the initial scene of the Argonautica Casino there can be seen some old Italian banknotes probably used to portrait an exotic foreign currency; their size is 2000 lire and 1000 lire. These were the smallest banknote sizes at the time, roughly equivalent to 1$ and 50c of 2013 - in 1998 the price of an Italian newspaper was 1200 lire.