Strategy one: Only attempt to develop one character deeply, perhaps two, but no more. This is the solution most good f/sf writers use. Critics who demand deep character development from all the characters in a short story don't know what they are talking about, they just want to sound smart.
Strategy two: Use super-efficient characters to whom your reader already relates. This is what Ray Bradbury and Stephen King usually do in their short stories. They use plain, ordinary whitebread Americans that they can develop in the fewest possible words. Both writers have an outstanding ability to develop whitebread Americans as deep characters. Their short stories often include aliens, wizards, demons, time travellers, etc. but these are seldom fully developed characters because developing them takes so many words that short stories would become novels.
My advice: if you can set your story in contemporary America and make your characters whitebread Americans use strategy two. If your setting or your characters must be more exotic use strategy one.
So while characterization is very very important, at some level your characters will all be similar no matter what you do, just by virtue of the fact that they all came out of your head.
Personally I think all my characters in my 1st person stories are wildly different from each other, but perhaps to an outside observer who has read enough of them, they will see the same types emerging often. I don't worry about it as long as I have honestly tried to create a unique individual.
The first problem would be one of character development. How radical should the change to the character be by the end of the tale? Here I would say that the character should have given up something that was important to him at the beginning of the story. It is either no longer important, or it is of secondary importance to something else he discovered during the story. Since you understand character development, you probably understand it better than I do.
The second problem would be of understanding people different than you. How they talk, think, and act. What are their values. For this, I would suggest looking at some personality books like "Please Understand Me." Or, much better, gather as much information as you can about actual people, through biographies, observation, and fiction.
Alas, I do not have any easy answers to either of these. I'll be keeping an eye on this thread to gather what I can, too.