Character mistake: At the beginning of the movie, Bill Paxton is pulling out documents out of the safe, maybe destroying some of them. Extremely unprofessional from an archaeological perspective. Although he represents a private company on a Russian ship searching for a diamond, he for sure violates many international laws with this brutal act of recovering objects. A professional treasure hunter should know that, plus a camera is filming him. He risks never getting a licence for a treasure hunt again.

Titanic (1997)
1 character mistake
Directed by: James Cameron
Starring: Bernard Hill, Bill Paxton, Billy Zane, Kate Winslet, Kathy Bates, Leonardo DiCaprio, Victor Garber

Continuity mistake: When Jack and Rose are going down with the ship, there is a man holding onto the flagpole. The man's life jacket disappears and reappears. (02:42:42)
Cal Hockley: You're going to him? To be a whore to a gutter rat?!
Rose: I'd rather be his whore than your wife.
Trivia: Gloria Stuart (old Rose) and Kate Winslet (young Rose) were the first two actresses to be Oscar nominated for playing the same character in the same movie. Kate Winslet did it again in 2001, when she was nominated Best Supporting Actress for Iris - she played young Iris Murdoch, while Judi Dench played old Iris.
Question: How did rats manage to get on board?
Answer: In addition to the other answers, rats can easily get on ships by climbing the mooring lines that tie vessels to the dock and also go up unattended gangways. They can also use temporary overhead cables attached to ships while in port.
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Chosen answer: During the several years it took to construct the ship probably, or in any of the supplies/food brought on board, or in the furniture brought on board. A single pregnant female rat can be responsible for thousands of rats in a very short space of time (the offspring are not too choosy about who they breed with).
Soylent Purple
A pregnant female rat could have made a home in a underneath a third class couch and had the other rats then all the females would have baby rats quickly.