A bull is agitated on purpose on several occasions, such as having a rubber band shot at its testicles. A blink-and-you'll-miss-it piece of text later in the game confirms the bull also died at some point
One mission also involves setting a bird on fire, to "create a phoenix", and another involves knocking down pidgeons with your board mid-air
The Skatetopia level in Classic Mode has a goal to grind off dead skunks from rooftops; they're portrayed in a cartoon-y way, with visible green stink lines, and simply disappears when grinded on.
Some animal bones are also scattered around this level, possibly being implied as being eaten by Bigfoot.
A song on the soundtrack is called "Awesome R***", though it is censored like that in-game as well. The lyrics to it seems to be completely unrelated, and the title appears to be only for shock value.
The bull that runs around the Barcelona level will drop piles of bull dung in its path in real time. One goal involves using said bull dung as a makeshift skateboarding ramp.
One of the final cutscenes of the games shows a in-game rendered home video of Bam's dad on the toilet, looking for toilet paper. Nothing is shown beneath his waist
One character in the game is a 10-year old who says inappropriate things, in the style of Cartman from South Park, and he tries to hit on an adult woman in a cutscene at the end of the Barcelona level. He is rejected and slapped by her, and is also voiced by an adult, so its less creepy and more low-brow humor
The cutscene after beating Boston shows a man in a portapotty being thrown into the ocean, and is never seen again, though most likely not actually murdered due to the light tone of the game. Your character can also fall into water, with text saying "I'm drowning", but you'll respawn on land unharmed.
One message says someone might have died during a stunt. There are characters who get into incident where they would be dead in real life, but the game runs on cartoon logic and they're probably fine
One special trick is called "Beaver Blast", which involves shooting fire from your ass, and has to be done in the Australia level to beat the game. Custom created tricks can include sound effects, which includes a farting sound.
In the Berlin level; you have to break the wall in a bombed church to let out the spirits trapped within. There are also souls of the damned in the Hell part of the Pro Skater level, though they appear as humans with long beards.
The game begins with a fakeout, where you and several other skaters are tied up in a warehouse and being attacked with a chainsaw. This is however revealed to be a prank
Some of the Jackass stunts can be seen as mild forms of this, such as people getting mouse traps thrown at them while in their underwear
Some animations when bailing while grinding on rails have you land on it with your crotch. A cutscene shows a man getting hit in the crotch with a tennis ball launcher. Various unlockable skating videos of bails include people hitting their groins on fences and such.
Barcelona and New Orleans have goals involving killing birds, for some reason. A blink-and-you'll-miss-it shot in a cutscene at the end of the New Orleans level implies the bull from the Barcelona level also died at some point.