"Alright guys, we've got enough money in the effects budget to make President Kennedy say one thing. Any ideas?"
If it were just these two iconic moments, it would be easy to dismiss this as a mere weakness for the poop joke's more penis-y cousin. But Gump wasn't the first Hanks character to pull the "'I've gotta pee.' --sneaks off to explore secret house" gambit. In The 'Burbs, Hanks uses the same excuse to investigate the home of his creepy neighbors.
How Tom Hanks lets a room full of adults know that he has to pee.
And in the art-house movie Road to Perdition, he uses his overactive bladder as a spidey-sense when he escapes a hit man by excusing himself to take a whiz.
OK, this is still The 'Burbs. The footage of Hanks grabbing his penis in Road to Perdition wasn't nearly as funny.
When Tom Hanks is actually urinating onscreen, you can be sure that something thematically significant is taking place. In A League of Their Own, it establishes his character's central conflict as a man who refuses to accept people without penises into the locker room. In another early comedy, The Money Pit, his literal pissing contest with a statue is the central symbol of his character's journey.
At the start of the film, Hanks and his wife optimistically buy an old house, and set about pragmatically dealing with its problems. For instance, when the toilet's plumbing doesn't work, Hanks merely goes outside to pee.
When he notices the plumbing is giving the statue in the front yard a fitful stream, he wryly asks if it's having prostate problems while his manly stream continues to flow freely. Here is a man with a world-beating attitude letting the world know in the only way Tom Hanks knows how: peeing on it.
Later in the movie, the house makes Hanks pay for his arrogance by ruining his marriage. Or, translated into Tom Hanks pee stream logic: The pisser becomes the peed on.