Epileptic Trees: It's never explained how Seto and Ren are immune to the effects of the Class Cage. Also, who was the voice speaking at the end before Shin and Sai faded away? And what exactly is that recurring mask creature?
Note most of this was answered in an interview with the developer back in 2009 two months after the Japanese launch.
Fridge Brilliance: You know how cats are a big thing in the game? Well, cats are known to be rather empathetic, if you earn their trust. They can understand your feelings without having you talk to them - they just know. It reflects the Glass Cage's purpose: to understand others without words!
Fridge Logic: How is it remotely possible to transition from nighttime in the amusement park to mid-day instantly when heading to the hotel?
WHY THE HELL CAN WE NOT REPLACE PF and Crow's BATTERIES?
Considering they're machines, they probably don't run on simple dry cells. Seto probably doesn't have the time or knowledge to search for specific batteries. Besides, batteries have a shelf life and they may have long run out. Unfortunately, that brings up another piece of Fridge Logic: why doesn't Seto need batteries for his flashlight? Where would he even find them?
Energizers. They keep going and going...
Seto has never been outside the observatory where the old man raised him, so he probably doesn't understand what a robot is, and that they would be fine if their batteries were replaced. He did ask PF what he should do, and it never answered him as if it were impossible.
Goddamned Bats: Not actual bats, but crows and ghost owls; some non-avian enemies also qualify. May double as Demonic Spiders, depending on the player.
It's more likely a really affectionate bromance, considering Crow thinks all friends kiss each other and doesn't seem to realize he did anything weird.
One could be quite curious as to just what book Crow was reading.
Scrappy Mechanic: All weapons will eventually break; the fact that a Random Number God controls it makes it such an annoyance, because a newly-purchased weapon just might be rendered useless following an enemy encounter. The inventory system may also get some flak: it's similar to the grid-based inventory of Resident Evil 4. You can arrange and rotate items as you wish, but it never feels like you have enough room, especially if you're packing backup weapons in case your primary breaks.
Tear Jerker: You may not cry, but you will feel the urge to; Seto keeps losing almost everyone he meets during the game, leading to many, many, scenes like Crow and PF's death, Sai and Shin's ascension...
The tearjerking mostly falls from the Memory Items, most notably the Torn Pictures and Withered Plant combination.
When Crow's battery runs out and the cutscene after it.