Overall, this was a pretty good episode. I wasn't sure how I'd feel about an episode centered around Plopper since like Brad Lascelle, I've never been a big fan, but I feel it was pulled off alright. I liked seeing the Bart/Lisa moment when Lisa regained her love for the saxophone and I also liked seeing Homer genuinely care for the pig. I agree there were some jokes that didn't work (the fairy getting its head cut off felt very FG, and the Mayo Clinic thing didn't do it for me), and they seemed to really like the misdirection gags (they're not a bad type of joke per se, but if I'm aware of how often they're being used, it's a bit of a problem), but HD-era joke awkwardness is not going away, so I can't make it a major complaint anymore. Otherwise I enjoyed this one and is the first episode with two plots (albeit fairly closely related) that I felt was on an equal footing with the single-plot Selman episodes.
Some little things I liked:
-I liked seeing a nod to Burly paper towels in the store at the car wash as well as the book "Killing Hannity", that made me chuckle.
-"Your attempts to enter the 21st century brought joy to no one" lol
-"Ah, how sweet. All the little children have-a the adult anxiety now" - it's sad that this quote is now biting satire. But as someone with anxiety issues, I like that they're addressing it in the episode (without making it too serious or too tasteless).
-Marge's exaggerated gasp
-"I will not subject him to something that has three vowels in a row!"
-Bart and Lisa "putting their heads together"
That and I'm probably the one person on the planet that never cared for Plopper / Spider Pig in any incarnation... be it here or in the movie.
You're not alone, although I will admit part of the reason I don't care for Plopper/Spider Pig is probably because of his popularity with non-Simpsons fans, so that's a bit hipsterish... (I remember when the movie came out in high school, my friends who knew nothing about The Simpsons and would never care to see the show were talking about Spider Pig and quoting Homer's song).