As they are helping the secret service agent remember the telephone codes pressed by the agent who took the football, audible tones are hears and Tobey tries to recreate. Cell phone do not have audible tones when buttons are pressed. Only phones that are wire-lined do this.
Gallo says that the nuclear football was handcuffed to a Secret Service Protection Detail agent. The nuclear football is actually handcuffed to a military officer holding the rank of Army, Air Force or Marine major or Navy or Coast Guard lieutenant commander.
In the intro, the two people manning the missile silo should be officers, not enlisted.