This list is incomplete, but you can help Encyclopedia SpongeBobia by expanding it.
Chapter 1: Employee of the Year
SpongeBob wins the "Employee of the Month" award once again, so Mr. Krabs decides to name him the "Employee of the Year." He then receives a mysterious mail package containing two free tickets to "Neptune's Pacific Paradise," and later gives them to SpongeBob for winning the "Employee of the Year" award, with SpongeBob saying they must of cost a fortune; however, they were actually free.
They get out of Rock Bottom, but SpongeBob and Patrick do some annoying things on the bus, so the bus driver tricks them and says that the bus ran out of gas. They get left behind and have to find a new way to get to Neptune's Paradise. The goal is to get on Sandy's rocket.
The oxygen fuel tank in Sandy's rocket runs out of oxygen (thanks to Patrick stepping on the gas pump), and they get stuck in Bottoms Up. The goal is to get the oxygen tanks filled at a place called Oxygen Springs so that SpongeBob and Patrick can get to Neptune's Paradise. But the real question is "where will Spongebob find a jacket?"
In the ending sequence, SpongeBob and friends get to Neptune's Paradise, but an employee tells them that the park is closed to make way for a private party, breaking SpongeBob and Patrick's hearts. SpongeBob and Patrick cry (although he was only yelling and banging his arms/legs on the floor as if he was having a tantrum). He says it's "SpringBoob SquirePin's" party, and Sandy tells him that he made an error in pronunciation. SpongeBob and Patrick are overjoyed as their hearts are fixed, and several characters that they met throughout the game jump out and say: "Surprise!" They all ride the rides and have a lot of fun. The ending shows them all leaving Neptune's Paradise, except Patrick, who is still on a ride.
Somewhere in each chapter, a mysterious character known as "Familiar man" is encountered. When SpongeBob notes that he has seen him before, the man denies ever having met him. At the end of the game, it is revealed that they are thousands of identical brothers, and that SpongeBob met a different one each time.
The outfit that Patrick wears throughout most of the game, (consisting of a green baseball cap, a lavender shirt, his usual green swimtrunks with purple flowers, and a camera), is seen on him in the beginning of "Neptune's Spatula."
If one clicks on the Operation Krabby Patty poster inside WSEA TV, SpongeBob breaks the fourth wall by saying, "Ooooh, Operation Krabby Patty, that was my very first game. Good times, good times."
Technically, this is not true because Legend of the Lost Spatula was the first official game to feature SpongeBob SquarePants. However, Operation Krabby Patty was the first PC game.
In Chapter Two, there is a man named Jojo fixing an antenna who asks SpongeBob for a soda and SpongeBob gets him a Diet Caffeine Free Coral Cola with a Lemon Twist; the drink is a reference to the episode "No Weenies Allowed."
SpongeBob has a pinup of Sandy in his locker at The Krusty Krab. If you click on it, he says, "Ahhh, Sandy Cheeks, looking at her makes me smile," hinting at a possible romantic connection between the two.
When the rocket in Sandy's Treedome is blasting off in the end of Chapter 3, there are two trees in the treedome. This is likely an error in scene production.
After talking to the Information Lady in Rock Bottom, she says, "You can check out any time you like - but you can never leave." This is most likely a reference to the song "Hotel California" by the Eagles.
The names of the two characters Marty and Nelson might be a reference to the actor and musician named Marty Nelson.