Broken Base: The arguments over "problematic" fiction, aspects with dubcon, noncon, incest, torture, etc. Whether the site's lenient policy and tagging system lets writers and readers consume these stories in a safe environment, or whether the site (and the writers) are promoting these behaviors and supporting actual rape. Critics feel that the fics endanger real life people and writers selfishly defend their behavior under tedious "free speech" declarations, while supporters argue that the idea that fanfic can lead to actual rapes and murders is just a disingenuous morality crusade. The argument isn't uncommon to fan fiction sites, but AO3's lenient policies attract these arguments in droves.
Jumping the Shark: Once upon a time, the fanfiction on AO3 were regarded as far superior to that on FanFiction.Net, because of accurate characterization, correct grammar, and proper use of warning tags. Now, with the influx of new writers on AO3, a good number of the fics there are just as lacking in character plausibility, comprehensibility, and trigger warnings as those on FanFiction.Net.
Misaimed Fandom: The tags on AO3 were initially intended for readers to filter works, characters, pairings, and triggers, but writers have developed an irritating habit of inventing irrelevant "fun" and "cute" tags and including them on the tags list for who knows why, much to the consternation of readers.