Asspulls are bad because they make the reader stop and say something along the lines of, "Now hold on just a freakin' minute! Where the hell did that come from?" Even a small asspull can knock a reader so far out of the story that they won't want to go back into it. A big one will make them throw the story away and tell their friends not to read it—ever.
Asspulls stem from an author's failure to properly anticipate his story's direction and needs. A good writer will know (at least in general terms) where he's going and what he requires when he gets there—and will lay out all his details and tools along the way so that when they are used, no one will go, "hey, wait a second, where did that come from?"
This is Chekhov's Gun worked backward—if you know you need a gun to go off in the third act, make sure you hang one on the wall in the first act. If, for instance, a Fan Fiction writer knows that for his plot to work Harry Potter needs to prove he's the descendant of a Founder, he'd best show him finding that out at some point before he needs it. It's not necessary have to actually say what he finds—the author can hide it from the reader, as long as enough surrounding detail is provided that when Harry pulls the the information out, your reader can say, "Oh! So that's what he learned back in chapter 6!" and not feel like they were somehow cheated by the author. The author can even hide it from the character who needs it by giving it to him in a form that requires interpretation, decoding or unlocking, which can then be done at the appropriate key moment. ("Harry, where did you get that ring?")
If an author avoids an Ass Pull with sufficient skill, the reader will probably say something along the lines of "that's very cool". The author should strive for that reaction.
Toward this goal, the author needs to be aware of how his story is going to end, and make sure that all the pieces needed for that ending are visible in the story along the way. They don't all have to be obvious—in fact, it makes for a far better story if they're not—but they must be there, in one form or another, or his readers will rebel.
This is especially true when—as is common for fan authors—writing a long-format story in installments. The author will usually not have the luxury of being able to change chapter 1 to include a gun when he realizes that he needs one while writing chapter 12. He must either plan out what he'll need so he can account for it ahead of time, or he must make do with the details he's stuck with when he gets to that point.
In all fairness, it is possible to write a large story without long-term planning. Charles Dickens did it almost all the time. He created his novels as serials, written and sold to newspapers one chapter at a time, and he had only the vaguest idea where they were going, if that much, when he started them. But those chapters were so dense in detail that he had literally hundreds of choices he could pick from when looking for something to turn into a plot point later, if/when he needed it. If the author is skilled enough and writes just as densely, he can pull it off. But a beginning writer probably shouldn't try it.
(Text adapted from A Fanfic Writer's Guide To Writing by Robert M. Schroeck, with the permission of the author.)