Logical flaws in the movie? Take your pick!
First of all, the Matrix is a program right, well, unless the programmer programmed it so that if you don't believe in the laws they don't apply to you, there is no real reason why Neo should have his powers. Did the programmer do that? Please tell me.
Secondly, the way people bleed from their mouth in the real world is when they get shot in the matrix is ridiculous. It's physically impossible.