Part of me wishes they used that badass compound bow from Thor rather than the weak looking "folding" number he used in this movie that wouldn't likely throw an arrow twenty feet, let alone accomplish the kind of accuracy he achieved throughout the movie. Pulleys and wheels just make everything better. And also, arrows don't work that way, flying straight and and flat like that. "Straight as an arrow" is a misnomer, since they wobble like a sonuva***** in flight.
Yeah, yeah, this is a movie with an Asgardian "god", a flying powered armor powered essentially by magic, a Hulk, and a gravity defying supercarrier that can turn invisible, but suspension of disbelief doesn't work as well for less fantastical elements in a fantasy.
Also, I read somewhere Jeremy Renner actually practiced how to do archery when prepping for the role, but Whedon or some other member of the production team didn't let him use the technique. That's a shame. I haven't done archery in years, but every time he shot something I was all "That's not how you draw a bow!"