In room 750, Spooky says "And you've got an axe! Nice." At first you'd assume that this is simply Spooky being sarcastic again, but the second time she decides to comment on it is during the ending where she makes you a specimen. Based off what else Spooky says here, she legitimately approves of the axe and how you use it, hence why she makes you a specimen. For bonus points? Back at room 750, she removes your ability to sprint but gives you unlimited stamina with the axe.
Even better, the factor in what ending you get is determined by how much you used the axe. If you kill a deer in Specimen 8's forest and chop down Specimen 1 a lot, you get the specimen ending. Spooky makes you a specimen because you've proven to be Ax-Crazy.
By removing your stamina and giving you the axe she's also turning you into a slow-moving specimen, which can be much more scary and dramatic.
The fact that somebody else, that person being the Old Man also got a weapon in the forest, can cross into Fridge Horror territory, as that person also became a Specimen, albeit as a result of possession, it could be that Spooky has a stock of weapons that she leaves in the forest in an attempt to try and convince people to act violently and get killed by Specimen 8 or suffer the same fate as the Old Man and you in the Bad Ending and become a Specimen.
Actually, that was Specimen 12's doing. Specimen 12 is the mansion. The old man was just a host.
Specimen 8 (nicknamed the "deer god") is particularly effective against violent subjects, according to its CAT-DOS entry. One thing that is important to note is that it is invulnerable, at least to the axe the player obtains in its forest. Yet, the deer that attacks the player inside said forest (which 8 lovingly calls its children, and has a Berserk Button pressed when you manage to kill one) are perfectly able to be damaged and slain by the axe. Its very likely that a violent subject would murder the deer and try and attack 8 as well, and pay the price for their efforts.
A few of the specimens are stated to be more effective against people with mental issues, including having a Dark and Troubled Past. Of course they're further in the mansion... the previous specimens would make them that much more effective.
When you think about it, Tirsiak's cute appearance can actually be explained in-universe. Her cute, innocent appearance would attract humans from her beauty like a Siren, allowing her to then lure them into predator-rich areas (in this case, Wolves), and have them chow down on the victim. So, despite her cruelty towards humans, she was feeding her "children" by luring food to them.
This actually would also explain why Unknown Specimen 4 has an anime design.
Specimen 6's face and design was based on the Happy Masked Salesman from Majora's Mask. Guess what has 6 letters: MAJORA.
The Devil-based monster appears in a fast food restaurant. The people in there would be making the Devil's Food
Why does Otto slow down when you look at him? Because the series he's inspired by has the rule of animatronics not being able to move when being watched. He might be a specimen, but he's still a haunted animatronic.
The Ghost Cow/Monster 5's design at first glance may seem odd; an upside down cow with limp legs held up by a mouth/eye creature, and in general seems out of place for the hospital. However, it's worth noting that symptoms of Mad Cow disease range from the deterioration of the brain, to infected animals being unable to stand. The former symptom ties into the idea that the entity is responsible for what happened to the hospital, as does it's death screen showing a brain while a set of words form an acronym for "forget," something the hospital staff said they would experience inexplicably.
The maze itself could also be a nod to the Minotaur's labyrinth, again helped by the idea of the monster being a cow or bull.
Looking through this, it occurred to me as to why the player character would listen to Spooky after either of your deaths. This could just be this troper not being attentive, but why would they :be in Spooky's ghost army or be a Specimen? Yes it was a tragic death, but thanks to her mechaniations so while the endings aren't meant to be seriously, there's nothing to stop the character from saying Screw This, I'm Outta Here! to her, especially since as a Ghost or presumably Specimen, she can't do anything to you.
Unless through becoming a specimen, you are blinded by blood lust and thus open to her influence, and as a ghost, Spooky is able to bind you to her will.
Or, as Endless mode seems to imply, the player character's soul is still stuck in Spooky's Mansion- the death message has notably changed to: "Your soul wiggles in agony" instead of "Your soul wanders the maze for eternity", implying your soul has already suffered that fate, and defeat is just a new day of torture. The player died, and didn't join the army, just like the romantic. The mansion is, however, built to contain ghosts and other horrors and prevent them from escaping (otherwise why do all the other specimens remain?) so it likely does the same to the player. Endless Mode is just a post-game player trying to escape the mansion, perhaps inevitably stumbling upon Karamari Hospital.
The presence of Monster 1 in the hospital becomes this once you realize it appears to be a police officer or security guard. Just what was he doing down there, why was he down there, and what could have happened to turn him into that? The fact he appears to not be one of the note writers from the hospital doesn't help.
Monster 4 has often been compared to a child. This itself has several implications, but there's also the fact that it's first encountered hanged in the Isolation Zone. The amount of questions this raises from why it's even hanged, why it's down here or what happened to the thing before it became a monster.