What qualities make a good fanfic?  What qualities make a bad fanfic?  

Really its opinion.  My opinion: characterization helps, so does having 
characters remain true to their original idea (why would Ranma ever 
arbitrarily attack Akane?), I like comedy (but its not nessecary),  I 
like a story (not a script) . . . blablabla

Is there
any sort of quantifiable that beginning writers can use or is it simply "I 
liked that one."?  

"I liked that one."

How much of it is mechanics vs. type of story vs. genre?

mechanics = continuity, writing style, etc.

As long as its not big gapeing holes in the continuity, I don't think 
continuity is too important.  Writing style has everything to do with it, 
a good writer can make being bored in study hall an interesting topic. 
(writing style is also completely subjective)

type of story = crossover, continuation, lemon, etc.

I'd read anything that cought my attention.

genre = Ranma, AMG, BGC, etc.

This matters only as an audiance filter.  I'm not reading a fanfic that I 
don't understand (eg, I've never seen Sailor Moon so I usualy skip on those 
fanfics).  blablabla bla blabla bla

What it all boils down to is: can you entertain me?  Thats what makes a 
good fanfic.

Matthew Trotter, coming soon to a theater near you.