The "slice through ninjas like fruit" bit in the TMNT vs. Renaissance Masters battle certainly counts: the banana in (the artist) Donatello's hand is so clearly Photoshopped that it's translucent.
After Holmes drops his killer punchline in his rap battle against Batman, Watson can be seen stepping over a railing in the background, revealing that it's actually a greenscreen.
The scene of Bill Nye walking into frame as he says "And I'm still in my prime" doesn't start offscreen, meaning that he literally just blinks into existence rather than walking into frame.
From the same battle, in his title card, when Bill runs across the screen holding a beaker, his shadow is very short and a bit deformed.
Not so much "special effects" as "camera zoom", but it still counts: when Juliet stabs herself, because the camera isn't zoomed in enough, it's very obvious she just thrust the knife beside herself and was nowhere close to her chest. Said knife also completely disappears in the shot where she's on the ground dead.
When Walt Disney draws the Mickey Mouse logo, the sparkles he creates... really don't come very close to following the outline made by his finger.
Any time a small version of a character is shown to be standing on something (Stephen King having two small versions of himself on his hands, Isaac Newton on a book Bill Nye is holding, etc.), it's very likely that they'll look to be standing somewhat off of it, or just otherwise not standing in a realistic way.
During the "Deadpool vs Boba Fett" bonus battle, Boba Fett's jetpack tends to disappear from his body when he's doing certain dance moves. These are most notable when Boba's in the background dancing while in the foreground he's rapping. In his last verse its even worse, as it disappears from the one in the foreground when he spins around then reappears after he finishes.
When Frederick Douglass flips a coin in his battle against Thomas Jefferson, it's absolutely painful to watch it land - the heads side of the coin obviously changes, making it very obvious that the flipping was a separate animation that somehow they didn't consider altering to be consistent with the coin in Frederick's hand.
It's an audio effect rather than visual, but Steadman's line at the end of "Oprah vs. Ellen" is so obviously Autotuned that it's cringe-worthy.
In a wide shot, Julia Child sets a dogfish on her cutting board. It then cuts to a close-up where she appears to be hacking at it with her cleaver, but when we return to the wide shot, the fish is clearly undamaged.
Parodied in "Superman vs. Goku", as Superman spontaneously grows a gigantic third arm just for the sake of punching Goku as he's dissing the Off-Model animation of Goku's series.