Considering Fermat's Last Theorem went 350 years without being solved, it was bad luck it was solved 5 years after the airing. Star Trek IV mentions Leningrad. It happens.
For Richie's body, why not just go with an extra with some minor "dead" makeup if they wanted to mention advanced decomposition? It's very strange the way it's done.
A couple other parts are both amusing and annoying. They don't initially understand that an elevator might require pushing a button? They still push buttons in the 24th century. Also, no one knows what "room service" means.