Quest bits are set by scripts and the engine whenever quests are started, and cleared when the quest is completed.
Each quest flag corresponds to a quest, as displayed in the current quests dialog in the view panel. There appear to be 29 quest flags for Clouds, and up to 43 quest flags for Darkside, however, there is overlap in the form of additional bytes available to both. Extensive work and examination of the event files will need to be done to determine the purpose of all flags.
Clouds Quest Bits
|0x2||Collect Phirna roots for Myra|
|0x3||Rescue Celia from the zombies|
|0x4||Falista's Horn/Witch Tower Quest|
|0x5||Orothin's bone whistle|
Darkside Quest Bits
Like game bits, quest bits are mostly game specific. Clouds, in theory, cannot set or check Darksides bits, and vice versa. In practice, however, there is significant overlap. The first 29 bit flags (3 bytes + 5 bits) are Clouds specific, the next 43 bits (5 bytes + 3 bits) appear to be Darkside only, however it is possible (though not seen) for Clouds to set bits 30 and up, thus allowing it to set the Darkside flags. There are also 7 bytes beyond what appear to be the regular quest flags that may have additional effects, ie, with the Reaper, Sphinx, and Golem events. Additional details will be needed on these "extra" bytes which may or may not have any use here.
Lots of bits to investigate.