How would a short story be affected if the writer changed verb tense from past to present and back again throughout a short story?
The technique you are asking about is called "flashback." It can be very effectively used to support the development of plot in a short story. Reasons for use of the flashback device would depend upon how your story is presented.
After a character is introduced in the present time of the plot, a flashback might fill in background details that would help the reader to understand the character's motivation or reaction to another character or to an event in the rising action. A flashback could also give the history of an element of the plot of the story.
Examples of the flashback technique can be seen in books, films, and television shows. One of the first modern books to use the technique was The Bridge of San Luis Rey. The Harry Potter books adapted the technique into magical episodes called "pensieves."
Used skillfully, flashbacks can add interest and the element of surprise or suspense to a short story.