These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
A bit more subtle, but there were a few angsty episodes that worked a number on younger viewers, such as the aforementioned Challenger episode.
The abruptness of the cut in the middle of the Challenger episode is pretty scary- they're in class with Mike (their teacher) saying "A lady teacher's going up on the shuttle! I'm going to bring my TV so we can watch!" and all of the kids are cheering. Then, the very next thing we see is Punky rushing into her home crying. Wham.
"Urban Fear," an episode about a serial killer making his way through Chicago, causing Punky to fear for Henry's life. The entire episode is much darker than the show's usual output, and they never show the killer getting caught.
Tear Jerker: Punky pleading for Brandon to pull through in "I Love You Brandon" (and her subsequent empathy for the passing of the dog of a fellow pet owner); Punky's emotional pain following the explosion of the Space Shuttle Challenger ("Accidents Happen"); her goodbye to Allen in "Divorce, Anderson Style"; Cherie's catharsis upon visiting her parents' graves in "The Anniversary."
In the cartoon episode "Punky To The Rescue," tears stream down Punky's face as she feels that "I guess I wasn't meant to have a family" upon feeling that she and the kids will never find Henry who is lost in the swamp.
And the infamous Challenger episode, especially since it came out two months after the the disaster happens, so the trauma was still pretty fresh. On top of that, it was based on Solei Moon Frye's own reaction to the incident.
Ugly Cute: When Glomer turns Margaux's face into a glomley face in "Pretty Ugly" (animated series).
The Woobie: Julie (played by a pre-Full House Candace Cameron), from the episode "Milk Does A Body Good."
In "The Search," you just want to cradle Punky in your arms when she tearfully confides to Henry "I want my mother!"