Good on you for writing a fanfic- a lot of people don't have the time and/or patience for that- but, to be honest, it could use a bit of work. The plot is a tad overused... even if you are basing it on a game, throw another character in- Yoshi, Wario, even someone like Wart or Tatanga, just to spice up the plot! It doesn't have to be the same as Super Mario Bros. 3 (well, the first part was anyway)... make it different somehow!
Also, the thing about script fanfics is that they usually lack description. Write as if the audience you're targeting has no idea who or where the characters are. What does Mario and Luigi's house look like? How did Bowser get the Princess? What do the characters look like? I know most of the people here know already, but someone who hasn't played a Mario game will be completely and utterly lost. So, describing surroundings and characters can be an invaluable tool when writing stories. Also, you don't need to draw the objects in the story... simply describing them would work just as well, if not better, as it builds up a mental picture. A good story should be able to flow smoothly to a point where you can visualize it inside your head.
You might want to abandon the script style and go with the traditional quotation marks, but then again it all comes down to personal preference. Just listen to any advice that you are given, and eventually you'll become a brilliant author. :)
