A character will often die. Their death will not show any graphic details, and it is usually implied rather than shown, but it might be fairly disturbing for some viewers.
The story mostly revolves around a man attempting to harm three children, which is rather disturbing.
The main antagonist often threatens to hurt or kill the main protagonists. He never actually harms them too badly, but he often gets very close.
A man is possibly eaten alive by an alligator during a sequence where the narrator explains the difference between the word "nervous" and the word "anxious".
A character breaks down a door in a scene parodying "The Shining". This is mostly played for comedy, however.
There is a suspenseful moment in The Hostile Hospital episode where the antagonist tries to "scare someone to death". There is strobe lights and a "The Shining" reference. Pretty creepy for a kids show.
This show has the main characters in non-stop danger and misery with barely any time to catch their breath, this could be bothersome to many viewers.
The over -the-top quirky personalities of villains such as Olaf, Nero, Esme, etc, while played for dark comedy, could be off-putting to some viewers.
Even though this is a kids show, the underlying themes of the story are very disturbing. There aren't really any jump scares or anything, but there is a lot of dark humor present.
The basis of the show is that a man is attempting to either 1) Kidnap the main characters (Children, the oldest is 13 or 14), 2) Marry the eldest child (13 or 14 year old girl, but only for her money), or 3) Kill the children and take their money. Every possible situation ends with their deaths, though, so it is quite disturbing.
Multiple times throughout the show, the children attempt to reveal the main antagonist, but every time, they are brushed off. Finally, the children run away.
If one were to dissect the story and themes, they might be depressed or sad (Much like the narrator of the story is), but if people realize that this is a fictional story, and that this did not happen, then they shouldn't get depressed by the story.