Other mistake: When the Political Officer reads the orders, they're supposed to test the silent drive and return home "on or about the 16th of this month." Shortly afterwards, Jack Ryan is briefing Jeffrey Pelt, and asks "isn't it the 23rd?", meaning the 16th of the month is in the past.
Other mistake: When Ryan is being lowered from the helicopter to the Dallas, it is a raging rain storm, yet the helicopter does not have its windshield wipers on.
Other mistake: Even though Ryan was warned earlier that the water was so cold that you could survive in it for only four minutes, he doesn't even shiver while drinking coffee in his wet clothes inside the Dallas. This after plunging deep underwater from his fall from the helicopter and then waiting to be rescued and brought aboard by the diver.
Other mistake: When the sub is ordered to turn right, Ramius is seated facing forward and tightens his seat belt. When the sub makes a tight right turn, his coffee cup slides the wrong way. (01:00:01)
Chosen answer: They use it to wipe the grease pencil markings off the screens.
We called it "the Duty Roll."