What makes a good fan-fic?

[Clarke]

Yeah, don't use Hello Earth as an example of anything fan-ficy. It runs on different rules from Avatar, (a major one being transhuman AI) and you'd have to have a really good justification to get the two to match up, and even if you did, you'll almost certainly break something else. (If only because Mr. Morden and his associates break everything)

IMO, writing fanfic is all about which rules you stick to. Unless it's the point of the fic in some way or another (like AUs or crossovers) you should stick to the source's rules as much as possible. (With the caveat that one of those rules might well be, as it is in the case of Avatar, "Make it up, technobabble/explain later.") So canon characters stay in character, canon [plot] devices work the way they work in canon, and importantly, things established as impossible in canon don't happen. (Violating the last is a major indication of Sue-ness.) The work has its own established tone and sense of "appropriateness", and fanfic should stick to that, unless (as with most writing rules ) the author knows why the rules are there and knows precisely why they're being broken.

Though AFAIK, the reason the majority of fanfic is crap has nothing to do with the fact that it's fanfic, but because 90% of all writing is crap. It doesn't fail at being fanfic, it fails at telling a story, whether because the characters are wooden, the writing is structured badly, the plot is nonsensical, or whatever. (Or, even more annoyingly, the author can't spell or compose a sentnece/paragraph properly.) In original fiction, 95% of that is never published, and so we don't see it.

IMO, none of the above mean that fanfic can't be different, very long, or even completely bonkers, it just needs to carry over the "style" of the original. Harry Potter And the Methods of Rationality, for instance, starts out as very good fanfic, because it keeps the feel of the series, but shows how it's changed when Rational!Harry tries to mess with it. (I've not read to the end, but it apparently it becomes worse in that sense because it starts focusing on game theory and I-know-you-know-style exchanges, rather than the conventional elements of HP)

(Obviously, YMMV on all of the above.)