Note that this list is not comprehensive. I picked out a few examples of each kind of error or problem I found. Of course, not everything is a black-and-white issue; this is not a list of things you have to fix, but take each under advisement.
>Twilight Sparkle nodded, admiring the precise parabolic arc the horseshoe made as it traveled through the air toward the metal stake at the other end of the pit.//
This sentence might do fine in the middle of the story, but as your opener, it winds around a bit too much. You want to establish something simple and clear, even if it might ramble a bit, but it should at least have a consistent focus. Here, we start on Twilight, but the focus quickly shifts to the horseshoe and spends most of the sentence there. Twilight's more interesting; we're here for the characters, after all. I'd recommend splitting this into two sentences, so you can have a stronger, simpler hook on the character.
>She scooped up a shoe//
When you have a repeated action, it's often a good idea to acknowledge it or rephrase. Her, I'd recommend saying "another" shoe.
>Just throw the shoe//
>Twilight hurled the shoe into the air//
"The shoe" is getting used a lot. Here are two places where it'd have a clear antecedent, so you could just say "it."