Very nicely done and polished game!! id only get rid of the mouse aiming and just let it shoot to where you're currently looking.
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I actually like the aiming with the mouse, even though it doesn't add much value to the gameplay (currently), it gives you more freedom and slightly more difficulty.
You could use it in future levels (?) to deliver presents to higher windows, doors or perhaps children hanging on the ceiling or whatever.
Definitely not remove it, is my humble opinion.