In giving the question some more thought, "good" stories--regardless of the show it's based on or the characters one chooses to write about--all start with the same, more empirical and less subjective elements. At my Han/Leia forum, we posted the following as a reference for readers who were frustrated because they wanted to leave thoughtful critique when they read something, but "just didn't know what to say/how to say it." We realized later that this was also a handy reference for beta readers and authors, to make sure that critical things were covered before submitting a piece for public consumption, since the "public" would be actively looking for these things:
So here is a partial list of the kinds of things to refer to when offering a thoughtful critique of a piece of fanfiction.
1. Plot - Did what happened in the story make sense? Was it believable? Did the pacing of the events match what was happening? Did everything get resolved, or were you left hanging?
2. Setting/Description - Did the author paint the scene for you, so you knew many of the elements of the setting as though it were a video playing in your head? Were the descriptions adequate for you to visualize what was going on?
3. Characterization/Dialogue - If canon characters were used, did their portrayals ring true? Could you see those folks from the movies acting that way, talking that way? If the author invented some original characters, did they fit in with the canon characters, become a part of the SW universe for you? Did the interactions among the characters SOUND like a real conversation? Could you hear their dialogue; did you even find yourself taking on one of the roles and speaking that person's words aloud?
4. Tone/Genre - If this piece was written to a specific genre, for example, angst, drama, mystery, action, or humor, did it meet your expectations for that genre? Did the tone match the genre? Was it "just enough", or excessive? If angst or drama, did it make you cry or cause you to become introspective? If humor, did you laugh out loud? If a mystery, was it suspenseful? Did the action leave you on the edge of your seat?
5. Imagery/Language Expression - Did the author use words artfully? Was the wording appropriate? Were descriptive passages painted so well you stopped for a minute and let your mind take it all in, creating the scene in your head?
6. Language Mechanics - Did the author check carefully for spelling, capitalization, punctuation and other grammatical errors?
7. Overall Effect - What was your gut level feeling about this work? How it it make you feel? Did you immediately want to find something else by this author to read?
Now as I said, this was written with Star Wars authors/readers in mind, but you can see how this can be easily modified to cover any fandom. I think all you'd have to change here is "movies" to "show".
The bolding and color change in #4 was my addition for the purposes of posting this here. The emphasis is meeting your expectations for a particular genre--if a humor piece, was it actually funny, etc. Because I get dismayed when I see people leave commentary based on something like whether or not they even like angst, or female pon farr, or whatever. Stories here are labeled. We give you a heads-up on content. It baffles me to no end how a reader will disregard a warning and read any way, then self-righteously leave blistering commentary slamming the story's very premise--but whether or not the premise was well-executed gets ignored.
The point is, a "good" story isn't defined by whether or not it's angsty, funny, action-packed, romantic, or whatever. There are both good and bad stories of all types. A "good" story is defined by how well the author did what he or she set out to do. It's not the goal that should be called into question, but whether or not they made it.