Unlimited weapons: When you get to the research center on Crimson (the big red place with a lot of "Mutons"). Buy a lot of parts for your weapon and finish the level with them. The next time you return to quest mode you should get the weapon parts you bought in the last mission. You can sell those and get new ones. You can still keep the old weapons if you finished the level with them. The same works for your Neo-Psionics.

G-Squad mode: Repeatedly fail a mission to unlock the G-Squad mode option, which allows the game to be played under an easier difficulty setting.

EX mode: Successfully complete the game to unlock the EX mode option. This option allows you to play the game again with the money available at the end of your last game, and unlocks new items.