What kind of stuff do you think on when you say "the game can be made better" ? coding or like the UI and art?
He have the gun because in level 3 he will be bullets and we able to shoot ;)
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For start background could be better, it seems kinda on the dull side. Jump could be more bouncy. Sprite animation done right would bring life to the character. Also you could impart some kind of story in the mix.
Then that's understandable thing to happen in a game jam. But two different sprites would work better if you consider working on it after the jam. Good luck!