They could watch the development of new nen abilities. Maybe some characters watch as Ging discovers new techniques or as Hisoka creates his unique and deadly attacks. Also, in fanfiction, they might watch events related to the Phantom Troupe. For instance, the characters could be observing how the Troupe members interact with each other during a heist or when they are facing off against hunters.
The Hunter x Hunter manga is unfortunately not complete. The author has faced various issues that have led to intermittent breaks and an unresolved storyline.