Hijikata, being an avid Status Lenses user, would want to check the weaknesses of the following monsters:

Demons
Soul Eater Books (presumably the same as normal books, but who knows, maybe there's something special about them!)
Roaming Candles (specifically, can a summer power holder just snuff their fire out?)
Snow Sharks (I assume they're weak to fire, but better to be sure!)
Floral Skeletons (related: can a spell be found in the library to simply make them - and the regular skeletons too - dead-dead instead of undead?)
Swishers
Jungulls
Explodies (specifically, can the Status Lenses read their elemental weakness even when their eyes are closed?)
Aerial Pirates
Lightning Reapers

Sorry for the laundry list, but you know how it is... those Status Lenses were expensive, so he's going to use them!