I think another example of a quirk could be when an anime sometimes has the same thing or idea appearing in many of its series that the studio has produced.
One example is Studio Gainax, who are famous for their 'Gainax Ending', which original stems from the Ending of the Neon Genesis Evangellion series.
An ending that doesn't make any sense, or does make sense but is hidden under enough Mind Screw to not have an easy explanation. This is usually a deliberate form of Mind Screw or intended as a Sequel Hook to a sequel that was never made. For whatever reason, after watching a Gainax Ending, you won't have any idea what happened.
After rewatching it, rewatching the entire series, discussing it with other fans, looking up the meaning of the symbolism, and subjecting the entire thing to a comprehensive literary analysis, you still might not have any idea what happened. If you're lucky, then there will be some kind of emotional or symbolic resolution even if it doesn't actually explain what happened to the characters, and you'll be left with the sense that the series as a whole was more deeply thought out than it seemed before.
If you're unlucky, then you'll be left with more questions than when you started and the sense that the series as a whole has been voided of the meaning you once read in it.
You can see this in Royal Space Force: The Wings of Honnêamise, He Is My Master, Monchromatic, and many other series made by Gainax.
More recently however, Kill la Kill (by Studio Trigger - where many of the employees are ex-Gainax ones) has one of the protaganists hoping that "Gainax doesn't screw up the ending"