Puddle is in some sad scenes, but he's there as a source of comfort to human characters and doesn't show any indication of understanding what's going on.
In the epilogue, one character begins to reopen a relationship with someone who was briefly but acutely abusive, but explicitly does not fully forgive her.
There are a couple individual instances of characters drinking too much, including one instance of minors drinking, but none of them seem to be habitual.
A main character could be on the autism spectrum, and was abused by one of their and siblings for being trans. The siblings become much kinder and more accepting over time, thankfully.
There are non-canon gag strips that acknowledge the comic, and in canon a few characters joke about events in their lives being improbably soap opera-like.
... Kind of? One male character enjoys crossdressing, and this sometimes leads to humorous shenanigans, but the story is very supportive of him overall.
Several trans/non-cisgender characters are misgendered, as well as one who identifies as genderfluid. An intersex character maintains she/her pronouns and that she is a cis female after initially being AMAB.
A 29-year-old impregnated a 17-year-old. Thankfully, the two broke up, and the 29-year-old is called out multiple times for his actions. The 17-year-old didn't even want to be in the relationship and was forced into it by her mother.