I drop most anime within the first episode. The way I see it there are more series than I could ever watch so I may as well look for quality. I also have done this dropping anime near the end. I did it with the Hyperdimension Neptunia which although had plenty of meh scenes I really liked (as is obvious from my profile). I recently went back and re-watched the entire anime to the end.
I was watching Genshinken. I got to episode 13 of I suppose 25 or 26, the art style changed which isn't neccessary a deal breaker, I dropped it since I've got nothing to watch currently I might try it again.
I been looking for any anime that references 'otaku' culture directly and it's slim pickings. I digress but I rarely finish an anime.
I did this with mass effect 2, dropped over 25 hours into the game right before the final level I was like, nope done.