Two big ones, both in-universe: the 9/11 scene, and the part where Happy tells children to call him so that they can donate to the people in Japan, who had been hit with a horrible earthquake and tsunami. Then there are the Libyan riots, the space shuttle Columbia disaster, the Sandy Hook shooting, and the list would just go on from there.
A year after the story's conclusion, a Robot Chicken episode showed a segment that was a parody of an actual Nick Jr. show, PAW Patrol, where the pups witness a 9/11-esque disaster, similar to what happened in one of the more infamous episodes of Happy Appy, described in the story.
Narm: Gets worse as the pasta goes on. See this example, which is a quote from the ending of the movie. "my demon slave has died for his unholy satanic master. Now I will kill or rape the kids I shall lay my eyes upon. Today is one day but the day after shall be a day filled with fear, hate and revenge. I shall come again and murder untill I am lifeless on the ground or on a rope. I shall create terror in mankind and Happle kind shall be legendary and be worshiped by all!"
Quite apparent in the message at the end of the film revealing the director to be Forenzik, and the sloppy attempt by the writer to explain how he called him Forenzik even though it was supposed to be the author's nickname for him
All of the fight scenes, partially just because of how blocky they are, but the award has to go to the final battle between Danny and Appy, which sounds sort of epic while picturing it, until you remember that it's being fought between a 7-year-old boy and a giant, anthropomorphic apple. You'll sometimes be asked to picture, for instance, the blogger holding a buzz-saw blade, a katana, a shotgun, and a knife all at the same time. Also, the fights with the fake Forenzik tend to include a bit of There Is No Kill Like Overkill that comes off as awkward, like blowing his head off with a shotgun, and then roasting the headless body in the oven.
Even though the non-original posts were deleted, the original entries still sound a little bit insane as the story went on. Toward the end, it sort of sounded like, even in the in-universe context, the blogger is making up or embellishing parts of it. For instance, when taking off to hunt down Forenzik, the blogger effectively offhandedly mentions that he brought a katana with him, but didn't mention the katana at any point beforehand and didn't explain where he got it from. The sheer amount of weapons he brings with him as well is worth noting, since they should have definitely hampered his movement quite a bit.
Looking at the rough drafts... let's just say that the story has improved. Case in point: the 9/11 scene originally had Tommy Wiseau in it.
Seasonal Rot: A variation. Later entries of the pasta get sillier, more over the top than they should be, and more poorly written, reaching deep of silliness. See "Narm".
Later, The True Vision stopped this trope dead in its tracks with the near-removal of narm and added posts and fixes.
YMMVs for Fright House Screamers:
Surprisingly Improved Sequel: Fright House Screamers is notably better than Happy Appy itself. It's more straightforward, much more realistic, and has a lot less narm.
YMMVs for Forenzik and the Forenzik Journals:
Surprisingly Improved Sequel: Forenzik is also notably better. You find out how sick Freddrick can really be, and it also ties a lot of loose ends together.
YMMVs for Dumb Angel:
Surprisingly Improved Sequel: When compared to the first three stories, Dumb Angel is considered to be the best canon Happy Appy story.
Seven people died from eating the apples.