Jason (von DarkMoor) said we were free to post in generalities about our slush reading, so I thought I would.
The single failure I see with nearly every story is the pacing, and the lack of getting to the heart of the story. In the case (genre) of heroic fantasy, I think that is very important.
Personally, I'm not one for pure action and plot. I like to get atmosphere and setting - but that can be imparted while action occurs.
Nearly all the submitted tales (that I have read - I only receive a portion of the pile) introduce the characters, have dialogs (or info dumps) about who and what their backstory is...then we get the monster...then the monster is dispatched.
I guess no one wants to show their hand early. I suppose some might be trying to build suspense. But the first thing I would do is start with the monster and someone battling it from the first word. "In medea res" - that is one thing screenwriting taught me. You can't waste film and budget getting the story going. The same can apply to prose - especially where action/adventure are the focal point.
Maybe it's a high bar, but I always go back to Robert E. Howard's tale, "The Black Stranger". That story had such a breathless violent opening - Conan hunted by and battling the Picts. While the following excerpt is not from the very first word, by the third paragraph or so (after Conan is described stalking through the woods, even though he is supposed to the hunted, not the hunter) we get this...
..the Cimmerian bounded into the path behind them and plunged his knife between the shoulders of the last man. The attack was so quick and unexpected the Pict had no chance to save himself. The blade was in his heart before he knew he was in peril. The other two whirled with the instant, steel-trap quickness of savages, but even as his knife sank home, the Cimmerian struck a tremendous blow with the war-axe in his right hand. The second Pict was in the act of turning as the axe fell. It split his skull to the teeth.
That is how you open a story in this genre, my friends!