I think one of the biggest pitfalls in writing short stories is adding too much detail, taking away from the plot and characterization. As writers, we tend to do that. This is one of the reasons why I hate penning short stories and generally avoid them: I love to write in depth on subjects. The creative juices flow and the such so much for me and other writers. You get a brainstorm and add a new idea, another new idea, and so on. This is why I enjoy writing articles more: I can keep the facts under so many words, generally, doing it quite well. With fiction, my imagination soars to the heavens...and beyond.
With many writers, unless they can severely restrain those creative juices, or focus them like a finite laser beam, it's hard to avoid the writing pitfall of adding too much detail, robbing from plot and characterization. With a short story, the trick is to find a good balance that allows the reader to be enchanted and enthralled by our written words, without taking too much of the story away. Words and phrases have to be chosen and crafted with more finesse, to create a story that will be read with interest and remembered, even if it is a short story (they can be not read and forgotten after the first page, too).
There are many great short story writers who have mastered this ability quite well. For many others, including myself, it's a hard process to finitely curtail those creative energies and juices when it comes to fiction. Amazingly enough, many of us start writing short stories. I did when I was a kid. But, how quickly many of them turned into short and not so short novels for all of us, as we all ascribed to higher and higher literary plateaus. We never quite realized that the mastery of the short story was one of those significant plateaus.
Other mistakes writers make are grammar and spelling. As a group moderator to an Internet group, people would be surprised to see how many very intelligent people out there have appalling grammar and make horrendous spelling errors. A lot of people simply do not write enough and their skills tend to atrophy. Even good writers are guilty of grammatical and spelling errors. With all of us writers, we have to constantly go over our work again and again till it is right, even if our eyeballs bleed. If we don't, especially in a professional representation, that editor is going to tear your work apart, word by word. A few errors are to be expected, but don't make them gratuitous.