Cheats can be unlocked in Super Mario Bros. Crossover by fulfilling certain conditions. Below is a list of all of the available cheats and how to unlock them.

Yes. There are some, so play the game to unlock them (or position the mushroom next to the "Enter Code" option and enter a certain code)!

Cheat Description How to Unlock
Level Select Allows you to select any level from anywhere Finish both games on Hard difficulty
All Ground Is Bricks Turns all ground peices into bricks Finish Super Mario Bros.
All Hammer Bros. Turns most enemies into Hammer Bros. Finish Super Mario Bros. Special
All Weapons Pierce Defeat armored enemies with projectiles easily Defeat 200 armored enemies and finish the game on any difficulty
Always Break Bricks Bricks can be destroyed no matter which form you're in Break 1000 bricks and finish the game on any difficulty
Bouncy Pits Causes characters and enemies to bounce out of pits Stomp 200 enemies and finish the game on any difficulty
Classic Simon Causes Simon's jump to become stiff, disabling air control Always unlocked
Classic Screen Scroll Prevents the screen from scrolling left Always unlocked
Classic Samus Prevents Samus from crouching and morphing into a ball while in the air. Always unlocked
Everyone Can Stomp Allows everyone to stomp on enemies Always unlocked
Evil Hammer Bros Causes all Hammer Bros. in a level to chase you immediately Defeat 50 Hammer Bros. and finish the game on any difficulty
Extra Checkpoints Adds more checkpoints in levels Finish a castle
Infinite Ammo Gives you unlimited ammo (includes SOPHIA III's hover) Collect 200 ammo pickups
Infinite Lives Gives you unlimited lives Finish the game without continuing
Infinite Time Removes the timer Finish a level
Invincibility Makes you invulnerable, allowing you to run through enemies Defeat 1000 enemies and finish the game on any difficulty
Water Mode Causes you to maneuver as though you are underwater Defeat 300 Cheep Cheeps