However, note that mentioning the killing of dogs *is* a running gag. There's also an entire Halloween special (Mr. Poofers Must Die!") dedicated to attempting to kill an imaginary dog, but nobody can do it.
there are vague hints at Señor Cardgage potentially being a kiddie fiddler in the Sbemail 'licensed', where Cardgage is known to own a 'shady daycare'. Strong Bad explicitly states that it is 'the kind that are open 24 hours and are surrounded by barbed wire'. This entire segment is played out as a joke, and Cardgage is not proven to be a paedophile.
In Strong Bad Email #119 "animal," Strong Bad imagines himself as a made-up animal with claws, horns, tusks, tentacles, a proboscis and segmented eyes. The result, dubbed "Monstrosity" by Homestar, could be considered body horror, but it's played for laughs.
One of Strong Bad's main character traits is his tendency to objectify women. However, he is depicted as being pathetic for this, and he never actually harasses anyone for it.
The Jibblies Painting, a painting which is found in Strong Mad's closet and appears uncommonly throughout the series, depicts a demon-like figure holding a torch.
In sbemail #159, retirement, Strong Sad is seen wearing a dress, as well as having a beard he normally doesn't have, likely a reference to the "bearded lady" trope.
In the Sbemail 'virus', Strong Bad accidently downloads hundreds of thousands of viruses on his computer by accident, causing the world's scenes, the characters and the website itself to become glitched and faulty.
In various scenes depicting the in-universe home movies in the Dangeresque series, titular character Dangeresque is shown to have a "nunchuk gun." This gun is never fired, either in "reality" or within the movie-within-the-cartoon.
Homestar and Marzipan, who are (sometimes) dating, are often mean or even violent to eachother - though this is usually slapstick in tone and played for laughs. Strong Bad is also often rude and mean to his younger brother, Strong Sad, which is also played for laughs.
In "Characters from Yonder Website," it's revealed at the end that the characters were drinking expired Smarty Juice, which caused them to pass out and hallucinate themselves as characters in the titular children's show. Strong Sad also joins in at the end. The Smarty Juice the characters were drinking could be seen as a type of drug similar to LSD/acid, but it's all played for laughs. (http://www.hrwiki.org/wiki/Drugs)
In "Homestar Enters The Spooky Woods" an illustration of a dead raccoon is shown and its more realistic than the rest of the shows art style so it can be jarring
A handful of scenes suggest that Homestar Runner shaves, however; this is shown to not be stubble but a puff of cinnamon he has put on his face to give the illusion of facial hair. Strong Bad claims to be growing a mustache, but this is a throwaway gag.
in "different town", strong bad mentions that he wants the king of town to be buried alive while surrounded by peas, and in "somber vacation", strong sad mentions burying himself alive in sand.
http://www.hrwiki.org/wiki/Buried_Alive
Marzipan and Homestar have an on-again/off-again relationship, but at least once Marzipan went on a date with someone else while it was presumably on-again.
On the rare occasion something bad happens that has lasting consequences, it's played for laughs (like the "deaths" of Strong Bad's various personal computers) and no one is shown to meaningfully suffer as a result for any extended period of time.
The King of Town, in Doomy Tales of the Macabre. In Where my Hat is At, Strong Sad is found at the bottom of a pool cemented in concrete, but he survives.