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.
Alternate Character Interpretation: Sigmund's nervous "Oh? Friends? Ahaha! Such happy for you!" was a brief unmasking of his haughty facade. Perhaps he was jealous of Kyle for having friends, which he—possibly—does not have (it would make sense, considering how arrogant he is) and decided to invite himself to the dinner at Kyle's house so he could humiliate Kyle (which he achieved, since Kyle admitted he was worse than him in the end) to make himself feel better? The aesop of the episode seems to support that theory—after Sigmund left, Kyle was in a defeated state, until Fanboy and Chum Chum assured him that he still has his friends, to which the reply was "Yes... I suppose I am the winner after all".
Ass Pull: The Dollarnator at the end of "Dollar Day".
Although this is a pretty regular occurrence being that each episode is another imaginary adventure and, well, they can. An example: Fanboy pulls out a glass eye equipped with heat vision in "Fan vs. Wild."
Critical Dissonance: Some people and reviews have given the show extreme backlash. That being said, the show won five Emmys (the most any Nicktoon has been awarded tied only with El Tigre), and it's premiere episode gained almost six million viewers.
Sigmund gathered a large fanbase long before he even made an appearance in the show.
Ho Yay: Tons. One instance is between Fanboy and Kyle in "Excuse Me". When Mr. Mufflin falls for their fake excuse note, Fanboy and Kyle grab each other's hands happily while they talk. They keep holding hands and smiling for a few seconds until they both pull away embarassedly.
The main characters constantly seem to have their arms around each other.
The entire plot of "Cold War" has Fanboy and Chum Chum fighting over Kyle in order to make each other jealous.
"Fangboy" has the duo intent on becoming "immortal companions". Fanboy, who believes he's a vampire, tries to bite Chum Chum's neck several times throughout the episode.
At the end of "Strings Attached", after Boog is turned into a frog, he yells for Lenny to give him a kiss.
In "Refill Madness", when Boog and Lenny finally manage to get Cuppy, they embrace each other for a few seconds while they say how happy they are until Boog shouts, "Stop huggin' me!".
And again in "Saving Private Chum Chum" and "Trading Day".
The whole episode of "Separation Anxiety".
In "Fanboy A'hoy", Fanboy and Chum Chum get a Spaghetti Kiss with a candy bead on a string. It's promptly censored by Chris Chuggy, but you can tell what happened.
In "Schoolhouse Lock", Fanboy and Chum Chum wander into a cave full of "carnival delusions" and go through the tunnel of love together. Kissing sounds are heard, and when they come out, both of them have lipstick marks on each other.
Idiot Plot: "The Last Strawberry Fun Finger". Not one person considers just splitting the Strawberry Fun Finger in half until the end.
In "Saving Private Chum Chum" Mr. Mufflin apparently forgets who Chum Chum is and mistakes him for a toy.
The Scrappy: A rare example where the main characters are examples of this. Fanboy and Chum Chum themselves are cited as the main reasons some people cannot stand the show, and a few opine that it may have been better off if somebody else was the main character (that somebody else usually being Kyle.)