Alternate Continuity: At the time in which the game came out, it was actually more or less in continuity with the Ultimate Spider-Man comics (and that's also how it was marketed). After some time, however, the comics went in a direction that couldn't support the game's events and a new arc was written that kind of paraphrased the game.
Amusing Injuries: Some of Spider-Man's quips lend to this. "Don't worry, nothing's broken except my spine... and ribs... and everything." is one such example, wherein he's thrown upside-down into a wall by R.H.I.N.O and peels off it like a cartoon character.
Artistic License – Geography: The map of New York City is fairly inaccurate, to say the least. A large section of the city is cut off (since it connects very closely to another part of New York) and Queens is depicted as the closest place to the city. Reason behind doing so is understandable though, Peter lives with his Aunt in Queens but operates out of Manhattan, so in order for him to 'go home' and include things such as his school, the two places had to be moved closer. Doesn't stop it confusing non-New Yorkers though.
Badass Normal: The Beetle and Silver Sable—the only two bosses fought by both Spidey and Venom.
Bookends: The first and final boss is Venom. The same background music even plays in both fights.
The Cameo: Venom's first boss is Wolverine from the X-Men.
In fact, there are cameos from all three of the other Ultimate series (at the time the game was made that is): Johnny Storm from the Fantastic Four, who you can race against, and Nick Fury from the Ultimates.
Canon Discontinuity: It's the other way around. The videogame synced very well with the comic at the time it was released. However, scheduling issues pushed the comic's adaptation further out so that the game's storyline finally was adapted into "War of the Symbiotes", it had to be in Broad Strokes to account for all the other story elements that were already in play.
Car Fu: Venom's weapon of choice, which is great against helicopters. Throwing them in free-range mode brings endless waves of cops down on you in a Grand Theft Auto-type mini game.
"Get Back Here!" Boss: There are several throughout the game, namely against the Green Goblin, Electro, and Venom.
Hammerspace Police Force: Triggering Venom's minigame causes wave after wave of cops to come after you. Rack up enough points by destroying stuff and killing enemies, and SWAT teams and eventually SHIELD show up. You don't get nearly as much regain from eating cops as you do civilians, which eventually stop appearing.
Heel–Face Revolving Door: Silver Sable goes from attacking Peter to helping him with the innocents to attacking him again until finally letting him get Trask.
In a Single Bound: Rather than web-swinging, Venom can leap immense heights to quickly get around.
Infant Immortality: Averted in a Take That towards the children who kept losing their balloons in the Spider-Man 2 tie-in game, in the form of a little boy with a balloon... who gets nommed on by Venom.
Power High: When Venom gains absolute control of his symbiotic suit.
Product Placement: Multiple billboards featuring the Nokia 3230 cellphone can be found in the game, as well as two Nokia buildings. Also, guess which brand of cellphones uses Adrian Toomes.
Punch Clock Villain: Silver Sable. She and her mercenaries were only hired to capture Venom, nothing more.
Regret Eating Me: Whenever Venom tries to eat a boss, they invoke this on him. He probably shouldn't try to consume anyone made of indestructible blades, anyone made of electricity, anyone who instinctively fires machine guns, or anyone formed of a chaotic spiky symbiote.
Spared by the Adaptation: In the Ultimate comics, Venom barely was originally barely a character at all, just a blob that was always hungry and which Eddie couldn't exactly control; here even without control Venom seems to maintain some intelligence, and Eddie learns how to control it. When the comic finally adapted the game's storyline, Eddie-as-Venom did get more development and gained additional control over the Venom Suit... but was captured by the Beetle and never seen again.
invokedTake That, Scrappy!: In the video game, Venom's tutorial presents you with your first task of absorbing people so that you don't lose health, your first target? A child holding a balloon. In Spider-Man 2, everyone hated the missions of helping kids who constantly lose their balloons.
Venom gains more health from civilians than he does from criminals or cops. He can also brutally kill enemies by slamming them face-first into the ground or snapping their spines like twigs.
Spider-Man can outright kill mooks in the game if you decided knock them off buildings, throw them into the ocean, or let a flaming car explode on them. Half of the City Mission side quest will even consider them successful.
Wanted Meter: In Venom's mini game, a little red bar appears under the health bar that serves as a wanted meter, with police, helicopters, the Wild Pack, and eventually SHIELD showing up in waves to take you down.
What Happened to the Mouse?: Unless you buy the special edition, you never learn what Beetle was doing attacking Spider-Man and Venom and what happens to him is never explained. He was collecting samples of superpowered beings for Doctor Doom.
What the Hell, Hero?: Spider-Man calls out Nick Fury (and Silver Sable, mistaking her as his employee) for not keeping Electro in custody.
Wide Open Sandbox: You can freely roam a shrunk-down version of New York City as Spider-Man and (once unlocked) Venom.
Window Pain: Venom's first boss fight is triggered when he throws a motorcycle through the front window of a pub. Said motorcycle belonged to Wolverine of the X-Men, who is understandably pissed off.
Logan: "That's my bike you smashed this place up with!"
Would Hit a Girl: Spidey and Venom's boss fights with Silver Sable, as well as the female gang members