Canon Fodder: Loads of it; for example, Gadget's past and the fate of her father has never been explored.
And what about what happened between Monterey Jack and Gadget's father? Or what Monterey Jack was doing before he met the Rangers (and how exactly he got those "cheese attacks," because they don't seem to me to be something he got from his parents [both of whom appeared during the show's run]).
Die for Our Ship: Poor Sparky. While he isn't usually outright hated, because he gets a Ship Tease with Gadget in the episode he appears in his existence has been known to make quite a few Chip/Gadget or Dale/Gadget shippers uncomfortable.
Fanfic Fuel: Most prominently, the scenes in "To the Rescue, Part 3" when Monty and Gadget talk about Geegaw, leaving the viewer with more questions than answers, and the end of "Good Times, Bat Times" which leaves the Dale/Foxglove pairing unresolved.
Fanon: Chip Maplewood and Dale Oakmont was coined by Michael Demcio in Rhyme and Reason; it's been used by pretty much every fanfic writer ever since.
To lesser degrees, there are more examples such as Gadget's coffee addiction or Tammy as a nurse.
There's also the death of Gadget's mother (who went unmentioned in the series, and has been given many different names) and father (who was only mentioned in the pilot). There's been countless theories created by the fandom, but pretty much everyone agrees that Gadget's mother died well before Geegaw.
Tammy as a nurse may have become canon, depending on how canonical one views the BOOM! comics.
Fan-Preferred Couple: The one great debate is not about whom Gadget shall be together with. It is about whether ("pro") or not ("anti") Gadget shall be together with Chip. No matter whom she'd end up with, if anyone, if not with Chip. The majority of fans, by the way, seems to be in favor of Chip/Gadget. Also, Dale/Foxglove. More obvious, but less debated.
Interesting side fact: Prior to the premiere of "Good Times, Bat Times", Dale and Gadget were the major Fan-Preferred Couple.
You'll notice not many people ship Gadget with the One-Shot Character Sparky, a lab rat and basically Gadget's equivalent to Dale's Foxglove; a one episode Ship Tease. This is basically the pairing pros and antis can both agree to dislike.
Ficdom: A few fans declared that they're bigger fans of the Fan Fic than of the show itself.
Genius Bonus: Monterey Jack is obsessed with cheese. Monterey Jack is also the name for a blend of cheese from Monterey, California. This leads to a little bit of Fridge Logic when you consider that he's Australian, but named after a cheese from California.
Fridge Brilliance: Both of Monty's parents (Camembert Kate and Cheddarhead Charlie) are travelers and adventurers. Maybe they were in Monterey, California once and named him then.
The voice Jim Cummings uses when he plays Monterey Jack's father Cheddarhead Charlie on the episode "Parental Discretion Retired" is actually the voice Cummings used to play Monterey Jack after Peter Cullen left the show. "Parental Discretion Retired" was one of the early episodes that had Monterey Jack voiced by Peter Cullen.
In "A Wolf in Cheap Clothing", Jim Cummings voices a Tasmanian devil. A couple of years later, Cummings would become the voice for theTasmanian Devil (as in, the Looney Tunes character)
Monterey Jack talked a lot like Steve Irwin already before the latter was even known outside Australia.
In the episode "A Lad in a Lamp", the genie is voiced by Dan Castellaneta. The episode predated Aladdin by three years and is funny because Dan Castellaneta would become The Other Darrin for the Genie in the Aladdin animated series due to Robin Williams having a dispute with Disney.
Ho Yay: Dale during the drag act in Adventures of Squirrelsitting. He's clearly enjoying his disguise and is flirty with both Chip, Monthy and even Fat Cat.
Monthy: I'm sorry, pallies. But Gagdet needs some cover.
Dale: No problem! (winks and rotates his shoulder)
And then there are the episodes "Adventures in Squirrelsitting" and "Good Times, Bat Times" where even more people are here for Tammy and Foxglove respectively.
Moral Event Horizon: Fat Cat crosses it in 'Adventures in Squirrelsitting' when he threatens to drop Tammy and Bink to their deaths if he doesn't get the Maltese Mouse and even when he gets what he wants he drops them. Thankfully, Chip and Dale are there to save them.
Foxglove from "Good Times, Bat Times". Foxglove has an entire website devoted to her (and now dedicated to her voice actress, the late Deborah Walley).
Tammy and Bink from "Adventures in Squirrelsitting".
Queenie from "Risky Beesness".
Sparky from "Does Pavlov Ring a Bell?"
Geegaw Hackwrench from "To the Rescue, Part 3" isn't even really a character, he is only ever shown on a picture. Yet, despite his unknown fate and total personal absence, he is quite popular in the fandom.
Anticlimax Boss: While the first game as a whole isn't too hard, a number of the bosses (including Fat Cat) barely move at all, and are highly predtaictable.
Even Better Sequel: The second game isn't as well known due to being released so late in the NES's, but it improved on the first in nearly every way possible, from graphics, to gameplay, to having a story that would not be out of place in a multi-part TV episode.
Game Breaker: In the second game, proper use of the fastball special makes most bosses incredibly easy.
That One Level: The final level of the first game greatly cranks up the difficulty. Most of the level takes place on conveyor belts that mess with your character's speed and make it difficult to move, which is especially troublesome during points where you have to make some difficult jumps with your moment hampered. There are no stone blocks for you to carry around constantly to protect yourself with. Not to mention that the enemies in the second half of the level have the ability to fire projectile weapons, and if they do they can destroy your boxes if you attempt to hide in them, which will leave you defenseless. Be prepared to die at least a couple of times before you finally reach Fat Cat.