As passengers are boarding the ship at Southampton a large sign is seen in the background which includes the wording 'authorized' or 'unauthorized'. This would have been spelled the British way without the 'Z', i.e. 'authorised'/'unauthorised'.
After the iceberg is sighted, the ship's helmsman turns the rudder to the right, yet the ship turns to the left.
Captain Smith is shown steering the ship in one scene. This task was usually performed by a quartermaster, not one of the bridge officers.