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.
Ear Worm: The Knuckles song: "How dare you try to infiltrate my home In hopes you may steal my precious jewels." Also, "Kill Sonic with a laser and then he'll be dead and I can do my evil stuuuff" set to Final Egg 2 from Sonic Adventure.
Heartwarming Moment: Oddly, involving the Tails Doll at the end of Volume 3. After Tails beats the possessed doll and throws it to the ground, it starts crying. Marine sees how sad it is and takes it in her arms, and after the credits it is shown happy to finally have a friend. You can even squeeze it with your mouse.
The ending of Sonic Shorts Volume 3 could possibly be the scariest moment. "Hello. Would you like to play? Come play with me. Play. Play." (doll goes demonic) "PLAAAAY. COME PLAY WITH ME MY CHILD. COME PLAY WITH MEEEEERRAAAAAR!" (doll lunges at screen, screen goes to static). The Tails Doll is arguably less creepy in his demonic form than his normal form.
Another one in Sonic Shorts Volume 4. After clicking on Knuckles enough times, a particularly scary short appears featuring Dr. Mario and Sonic.
To clarify: The short involves post-operation Sonic in Dr. Mario's office. After comforting Sonic and mutters "You're one of us now", he then offers him a lollipop. The camera angle then reveals the operation was a lobotomy, and as Sonic struggles for the sucker, the respective logos of Sega and Nintendo appear, the latter ending the short. Yikes.
In Sonic Shorts Volume 5, in one of the transitions between two shorts, you can see a faint image of Tails Doll, covered in blood and bearing sharp teeth. Clicking on this grants you the pleasure of seeing a dark alleyway with a flickering light as Tails Doll flashes in front of the camera. What's worse is that the shot looks like it was filmed from somebody's point of view...
Sonic Shorts Volume 6 has a Bubbles badnik after the credits. You can click on it to make it scream and release the spikes in its body, but the scary moment is the third time you click it, where it starts spewing blood as its spikes come out, giving a rather terrifying shriek as it fades away.
Subverted in Sonic Shorts Volume 7. Tails Doll looks like he's chasing Tails, trying to kill him. But, in actuality, Tails Doll was just trying to give Tails his ring back.
Knuckles Briefs introduced us to the Knuckles Doll, in a similar vein to the Volume 5 example.
Squick: Sonic and Shadow's reaction to a picture of them together on the internet. Shadow expected to see them duking it out to see who was the ultimate, but...
Another somewhat common joke is Eggman trying to be sexy, followed by Sonic reacting by dying, or just wishing he had Brain Bleach on hand.
"His eyes melted!"
In a skit making fun of the infamous kissing scene from Sonic 2006, Sonic notes that he can't tell which is more disgusting/creepier: The fact that Elise kissed an animal, or the fact that she kissed a corpse.
Take That, Scrappy!: Chris gets in a lot of trouble in the shorts. This has carried over to both Sonic F (which is done with slightly less frequency, but it's still there) and a 2012 April Fools My Little Pony: Camaraderie is Supernatural episode, which consisted of a toy Pinkie Pie running over the toys of the cast of Friendship is Magic... And a Chris toy along with them.