I think it's because the movie maker wants to show that humans make mistakes and forget things, even in dangerous situations. Peter is eventually internally a blend of two species. Sometimes it can happen that the human ability, rather than disability, can overpower the spidy sense. This should be an understandable event for the viewers if we accept seeing Spiderman in the movie. :P
They also wanted the viewers to feel that "Oh! Spidy has got hurt but still he is in mood to help every one. Such a nice fella."
These can be understood as if a human being is in the middle of some work with a huge pressure on him and suddenly something happens near him but he simply didn't notice it. The maker wanted to make the movie more real w.r.t. the earlier Spiderman movies so that he can include that kind of reality in the next Avengers movie.
I don't think it's a big mistake.
Nice notice anyways. \m/