Big-Lipped Alligator Moment: In the animated series's episode "La venganza de Tengo-Pis", equivalent to the comic book "El premio No-Vel", Filemón accidentally squashes a policeman's nose between two bricks (It Makes Sense in Context), so the cop starts hitting him with his nightstick. This happens just like the comic book, in which they would cut to another scene just after, but the series deviates from the source material by adding a strange scene. Seeing Filemón being defenselessly beaten, Mortadelo turns into a dog and tries to disarm the cop, managing to free his partner; the two TIA agents then attack the policeman, getting the upper hand by pulling his ear and flattened nose, and they stretch and stretch them (with the poor guy screaming in pain in a truly creepy way) until an explosion fills the camera and it cuts to Mortadelo and Filemón laughing. The incident is never expanded or mentioned again, and the viewer only gets the gruesome implication, rather out of context for the series's level of violence, that they ripped out his ear and nose or something worse.
"El gran sarao" had the chapter where Filemón and the Super wrongly assume that Mortadelo has turned into a Serial Killer who decapitates anybody he encounters. Amusingly enough, everything they see or find casually make it look like he is really a murderer.
There is a similar, ineffable scene in a different album, where Filemón's body gets absurdly tiny, almost invisible, because one of Bacterio's inventions, but his head remains the normal size. Obviously unable to stand, Filemón falls and gets knocked out. Enraged, Mortadelo picks an axe to attack Bacterio. In that moment, a completely oblivious Ofelia enters the room talking to herself: "Mortadelo and Filemón are always arguing, but it never gets that bad...". When she sees Mortadelo holding an axe, and Filemon's lifeless head on the floor, she totally freaks out.
At the end of "La caja de los 10 cerrojos", Mortadelo, Filemón and the Súper throw a huge box to the sea, after learning it is actually a surprise box and not a safe containing a giant diamond, which was what the three men believed and spent so much time working to find. In the next panel, it's revealed that the huge head that came out of the box contained the diamond inside after all. Some fishes comment on how excited would be the surface inhabitants if they found it.
In one instance, the pair has to enter the TIA offices by telling a password to a guard in the other side of the door, as usual. Filemón knocks on the door and tells the guard "Hi, it's us". Though the guard recognizes Filemón's voice, he refuses to open unless he hears the password. Filemón insists that the password is "that one", but the guard is adamant that he wants to hear it to grant the pair access. Turns out that the password is the whole Don Quixote book, that Filemón recites by heart.
Designated Villain: The one big flaw in "Objetivo: Eliminar al Rana" ("Objective: Get Rid of the Frog"). The titular characters are told by the Súper to become a Reverse Mole in Rana's organization and kill him before Rana kills the Súper first. However, Rana always treats the titular characters with respect (in stark contrast with the Súper), and he's never shown to be doing anything evil apart from trying to kill the Súper (and the exact reason for such harmful desire is never explained) until the very last chapter where he tries to kill Mortadelo and Filemón as well (and that's only after he's heard they're trying to kill him, so it would count as self-defense). This was so egregious that, when "El tirano" ("The Tyrant"), another story which could be considered a remake of the aforementioned story, was released much later, this time the author made sure to clearly show the antagonist as a Complete Monster.
Ethnic Scrappy: Black people are usually portrayed as relatively sane, civilized and well articulate. However, they are drawn like in a 1930's cartoon. Chinese people are a different matter - They are both drawn, and act, like in 1930's cartoons! Even Chinese space program engineers are portrayed as buckteethed gnomes who talk (and eat) flied lice!
Black people tend to come in two varieties. Regularly-sized, relatively slender fellows who are particularly civilized. And big, muscular men who are easy to anger. An album taking place in New York City included both varieties. Attempts of Filemón and Mortadelo to investigate Harlem and locate a suspected terrorist, constantly end with them beaten by various locals who seem to have white guys as a target for their wrath. When the two agents finally get their suspect, he turns out to be a leader of the community. Their information about a bomb was wrong. His "bomb" was evidence about political corruption, and how money supposedly going into urban development ended up in the wrong hands.
This is mostly due of a case of Values Dissonance. Albeit still present, racism is not nearly as big in Spain as in other countries, so this portrayals are seen mostly as Played for Laughs, with no ulterior motives nor messages, conscious or otherwise.
A particular joke on a series of cyclists said: "This one is red with anger, this one is green with envy, this one is yellow with liver problems, this one is black with... well, with his being from Tanzania, obviously..."
In an old short story, Mortadelo and Filemón are asked to escort a young African prince back to his country, after he has finished his studies in Spain. During the flight, the child causes trouble around the plane, and the stewardess asks Mortadelo, "Are you traveling with a boy of color?". Mortadelo calmly answers, "It depends. Which color?".
Franchise Zombie: The series has been accused of this since roughly the early 2000's.
"Funny Aneurysm" Moment: The current page image for this trope is a panel from 1992, in which a plane can be seen crashing into one of the Twin Towers of the World Trade Center.
One of their best stories is set in Germany, with M&F going all around the country in their mission (and successfully crossing the Berlin Wall twice!).
Interestingly, the parts where they cross the Berlin Wall were replaced with something else in the German edition.
Thankfully, the situation is now over and another publisher has taken up the slack to publish the series in Germany. The new publication actually is vastly superior to the first one, since that one suffered from a bad translation and sloppy work. The sales right away proved the series is still highly popular in Germany.
And in Denmark (as Flip & Flop). Ibañez even made a (pretty good) story set in Copenhagen in honor of his Danish fans, featuring the Little Mermaid Statue as a main character.
Growing the Beard: The comic was an entertaining weekly strip with the traditional few-panels-and-punchline formula, but it wasn't until their first full book, El sulfato atómico, that the now standard supporting cast appeared, allowing for deeper storylines and better interactions for the protagonist duo. Ibáñez's drawing style also evolved notably, imitating somewhat that of Hergé's Tintin.
Seasonal Rot: Most fans agree that it's been going on since The '80s, though very occasionally a decent album still appears (La Sirenita is one notorious example).
Most non-white characters are drawn and speak as typical wartime caricatures, complete with accents, which raises more than a few eyebrows in the present day. That said, Ibañez's black characters tended to be universally more competent or at least less suicidally stupid than the white protagonists, so maybe it was just him catering to the drawing style expected at the time.
The traditional Spaniard sentiment of disdain towards authority really shows in each album, starting with resident Bad Boss El Súper, who is by far the greatest Jerkass. Real life politicians, wherever they show up, get absolutely no quarter.