Port Or Starboard?
This one is actually not a mistake – but an alleged mistake everyone believes to be true, when Cameron was actually right on the money. As the crew try to avoid the iceberg, they yell “hard to starboard” and “hard to port”, after which the helmsman does the exact opposite of what he apparently should.
But in 1912, port was considered the right side and starboard was the left side. This changed after a while, but in the movie Cameron got it exactly right, despite what people thought.