In the background during the diving scene, the klaxon diving alarm continues to sound repeatedly many times. However, in the real world aboard submarines of the US Navy, the diving alarm sounds twice to signal a dive ("oogah-oogah") or thrice to signal a surfacing ("oogah-oogah-oogah").
Though taking place on a Los Angeles class submarine, during one scene footage is shown of a Russian Akula class submarine opening its outer torpedo tube doors.
The argument about the location of the classified material trash can is a moot point. Classified material is NEVER stored in an open trash can. It must places in a properly secured container (i.e. safe) and then properly destroyed.
When changing depth to help a thermocline the order is given to the helm or helmsman to make depth 150 feet. This order would be given to the diving officer of the watch onboard a US Submarine.