The ship depicted as leaving the dock at the beginning of the film is named "San Capeador" on the bow. The ship depicted as docking in New York City has the name "Olympic" on the bow.
Right after the stern line is cast off, showing us the ship's starboard side is at dockside, the Captain (Walter Connolly) orders the helm, "Hard to starboard" - which would apparently send the ship right back into the dock. The 'Hard to Starboard' command by the Captain isn't a goof at all, as his very next command is 'Both engines slow astern'. In other words he's reversing the vessel and in that case starboard is the correct direction.