No submarine has air ducts that big, especially a WWII era model.
The sub was heard pinging her sonar while going to the bottom. If she was rigged for silent running he would not engage active sonar.
Blue denim Dixie cup hats were not worn in the 1970's. They were worn in WW2 and phased out in the 1960's.
Adm. Nelson calls Sparks to connect him with the Sec. of Defense. Later when Sparks calls Nelson back he tells him the Sec. of State is on the line.