I can think of a couple off of the top of my head:
-Alice Cooper asking Kermit to sell his soul to his "manager" (obviously implying that he is Satan). This one is definitely supposed to be funny but the subject matter alone is enough for me to consider it a dark moment.
-Crazy Harry in general. Sometimes I can't help but consider the possibility of him being a puppet terrorist. He's a psychopathic guy who has a disturbing obsession with blowing objects and even people up for no reason. Yup, that sounds like a terrorist to me.
-Time in a Bottle. Their beautiful rendition of the Jim Croce song has a very poignant message to it. Everyone at some point in their life will eventually come to that harsh realization that they are getting old. The song as well as the accompanying Muppet sketch perfectly captures that mixture of sadness and anger that most every person will someday feel when they realize how truly short life actually is and that no matter how hard they are, they can never just magically become young again.
-The Gambler skit from the Kenny Rogers episode. The titular Gambler Muppet dies in his sleep at the end of the sketch and comes back as a ghost. Do I even need to continue talking about this one any further?
-To me Marisa Berenson singing You're Always Welcome At Our House always seemed like a scene straight out of a horror movie. The fact that she kidnaps random people and even went as far as to stuff one of them in the oven and the creepy slasher-like smile she makes at the end of the sketch that would make even Jeff the Killer feel uncomfortable certainly make for a dark, non-Muppet-y sketch.
-While the Muppet sketch itself was very tame because they cut out the end of the poem, Rowlf reciting the t*t willow was pretty surprising considering they actually read a poem about SUICIDE on The Muppet Show. Yup, the real poem ends with the Dicky Bird killing himself.
-The Liza Minnelli episode which was from beginning to end a bunch of dark comedy involving murder.
-This one isn't dark per say but I need to talk about how unsettling this one feels to me:Mummenchanz. When I was a kid, I remember being super weirded out and disturbed when those creepy looking humanoids with strange clay faces randomly appeared on one of my favorite shows. They never scared me but I always felt this twinge of unease whenever I watched the Mummenchanz sketches that I admittedly still feel to this day. Seeing them surrounded by beloved Muppets only added to the creep factor for me. I can totally understand why YouTuber blameitonjorge added them to his "Top 20 Most Unintentionally Disturbing Children's Characters From Around the World" list.
-A group of male Muppet monsters repeatedly trying to tear off Sandy Duncan's skirt. For something lighthearted as the Muppets, the scenario I just described sure does sound an awful lot like sexual harassment.
-Speaking of the monsters, how could I forget Ruth Buzzi's rendition of "Can't Keep My Eyes Off of You" where she tries to get Sweetums's attention for the purposes of love but instead she gets knocked over a table by him. Domestic violence, much!?