In "Horror of the Haunted Hairpiece", Fred blaming Red Herring for everything practically hits its peak when he deliberately goes off-script during the summation and approached Red in his house just to point the finger. Red (who was much more interested in reading the paper) didn't even bother to look up when he told Fred to beat it.
The Were-Doo muttering over his crummy gifts during his birthday party:
Julie: I don't have it. I told you that an hour ago. I told you that two hours ago.
Ivan: Okay. I understand. (walks away) See you in an hour.
From the first episode, which involves Shaggy's prized bike being stolen by the Monster of the Week, we have this exchange.
Freddie: "Well Shaggy, Im glad to see you're taking this loss like a man"
*The camera pans out to show Shaggy lying on the floor, kicking and screaming over his lost bike like... well, a kid*
Fred is trying to go a whole case without accusing Red Herring of being the monster... turns out this is the one time he really was the culprit! Fred doesn't take it well.
As mentioned twice above, Fred's consistent blaming of Red Herring for crimes was a Running Gag extraordinaire—but in a prime case of Tropes Are Not Bad, watching the joke gradually get more exaggerated only made it funnier. In the first few episodes, Red being the culprit was feasible; he was often near the scene of the crime or at least had some motive. But as time passed, Red's connection to the mystery became more and more tenuous, until it was eventually nonexistent (for example, someone would point out that Red was on vacation and/or visiting his grandmother that week, so he wasn't even in the state at the time). But it never mattered—Fred would always accuse Red of being the Monster of the Week. Similarly, Red's appearances in proving his innocence got wackier: after the accusation, a telephone might ring with Red appearing on the other end and announcing that he didn't do it, or, as mentioned above, Fred traveling to the bully's location to make his case. It eventually reached Once an Episode status, and it was always hilarious.