Symbolism, Imagery, Allegory
Speaking of patriarchal authority… it's a bit, um, hard to have patriarchal authority without phallic symbolism, isn't it? The character most obsessed with the male member is definitely the Bastard.
Most of the Bastard's phallic imagery comes out in the paternity trial scene of Act I, Scene 1, in the form of various dirty jokes. For example, when the Bastard's half-brother asks, "Shall then my father's will be of no force / To dispossess that child which is not his?", the Bastard replies, "Of no more force to dispossess me, sir, / Than was his—" [nudge, nudge] "—will to get me, as I think" (1.1.133-136). Oh, snap!
Translation: When the Bastard's brother complains that his father's "will" is being dishonored, he's referring to the legal document expressing the desires of a dead person. But when the Bastard uses the word "will," he's totally referring to 1) a man's penis and 2) sexual desire. Basically, he says that Sir Robert Falconbridge, Sr., wasn't much of a man—and that he couldn't even use his, ahem, "will" (a.k.a. "willy") to have sex with Lady Falconbridge.
You get another example of the same joke later in the same scene, after Queen Eleanor has asked the Bastard to give up trying to get the Falconbridge land and consent to being known as the son of Richard the Lionheart. The Bastard agrees and then bags on Sir Robert Falconbridge some more: "I would not be Sir Nob in any case" (1.1.151).
"Knob" is a nickname for "Robert" (it's kind of like calling a guy named Richard by the nickname "Dick"), so the Bastard is saying that he doesn't even want to be Sir Robert Falconbridge's son. "Knob" is also slang for "penis," so the Bastard is also calling the guy a... come on, you totally don't need us to spell this one out for you.
So why is the Bastard so obsessed with the penis jokes? Well, basically, for him, the penis symbolizes masculine power, which he values more than anything else. Because he thinks Sir Robert Falconbridge is lacking a certain, um, potency, he would rather be known as the son of a more upstanding warrior—inheritance or no inheritance.
But it isn't just the Bastard who makes use of phallic symbolism. In the macho culture of King John, it's just second nature—especially in situations of conflict. For example, when Hubert is staking out his ground against Salisbury in Act IV, he probably isn't just referring to weapons when he says, "I think my sword's as sharp as yours" (4.3.84). We know you know what this dude really means. It's all about who's the bigger and better man, literally and metaphorically.