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.
Author's Saving Throw: With Stop 'n' Swop rendered impractical, but hints about it already dropped, Rare couldn't just ignore it. The solution was to add Banjo-Kazooie Cartridge enemies into Banjo-Tooie that drop the promised items when defeated.
Designated Hero: Parodied somewhat with Kazooie, especially in Tooie. Before the game even starts, she's shamelessly cheating at cards with Mumbo and Bottles, then spends the game constantly snarking and demanding jiggies from characters in trouble before letting Banjo rescue them. One of Banjo's recurring lines is a shocked "Kazooie!!!" in response to these moments.
Mumbo Jumbo from the first game. Started out as a weird shaman with an unexplained romantic history with Gruntilda who turned up in a handful of levels. In the second game, he became a playable character.
Jolly Roger, making him (along with Mr. Fit) one of the few minor characters to return for Nuts & Bolts with an expanded role.
Chili Billi and Chilly Willy are one of the most popular bosses from Tooie. For one thing, they're two boss fights instead of one. Said boss fights are also quite enjoyable. They have some of the most impressive visual effects on the N64. Also, THEY'RE GIANT FREAKING DRAGONS.
Mr. Patch is probably the other most popular boss in the series. He's easily the single biggest enemy in the series, bar none, with his arena alone being larger than the entire first world of Banjo-Kazooie. He's also fought entirely from the air. To top it all off, he's hilarious. These factors have all made him very beloved.
Even Better Sequel: Banjo-Tooie was a significant improvement over the original, expanding on the formula by dramatically increasing the world size, adding more bosses, and making Jiggies harder to find, to name a few.
Evil Is Sexy: Let's just say that Grunty becomes really beautiful when she absorbs Tooty's youth in the first game-over sequence.
Most of the enemies in the original game are reasonably easy to defeat, but the giant snowmen that appear in a few levels are incredibly annoying in that they can only be killed while you're in the air (and require a special maneuver that's easy to bungle) but still present a danger while you're on the ground.
And those ghosts in Mad Monster Mansion; no golden feathers? You're screwed.
The Hotheads in Banjo-Tooie like to swoop in on their flying carpets at inopportune moments, often knocking unfortunate players off ledges, and their airborne nature makes them difficult to hit. Their annoying laugh just adds insult to injury.
Also from Tooie, the Minjos. While it's fairly easy to tell when a Jinjo is actually a Minjo (if a Jinjo is in a spot that's way too convenient for you, it's probably a Minjo) they're still very fast and aggressive and, unlike most enemies in the game, tend to require more than one hit to defeat.
Good Bad Bugs: In Tooie, Banjo can double-jump when he's going solo by swinging his backpack in mid-air and then jumping again. This move allows for minor Sequence Breaking by reaching otherwise inaccessible platforms without outside help.
The Lord of Games from Nuts & Bolts, for shamelessly dissing one of the greatest features in the past two games (via his "Collect-a-thon"), and radically changing the formula of the game himself.
Seinfeld Is Unfunny: A weird instance of this trope. The original Banjo-Kazooie was widely felt to have caused this trope to apply to Super Mario 64 — at the time considered the benchmark for 3D platformers — which many reviewers in 1998 claimed looked outdated and inadequate compared to Banjo-Kazooie. Fast-forward to the modern day however, and the situation is reversed. Super Mario 64 is still very fondly remembered by most, whereas Banjo-Kazooie suffers from being lumped in with Rare's subsequent collectathon platformers.
Squick: Everything Brentilda tells you about Grunty in the first game. The hag's pretty much built on Squick.
Though the Scary Striptease doesn't seem so bad if you think of Gruntilda as she appears in the Game Over screen doing it.
Stuck In Their Shadow: Banjo-Kazooie is a little weird about this. Ask anyone who the star is, and they'll say it's Banjo, even though the titles of three out of five games also include his partner Kazooie. The second game, Banjo-Tooie, opts for a silly title pun instead of recognizing the second lead's name (it's even lampshaded by Kazooie herself at the end of the first game), and Banjo-Kazooie: Grunty's Revenge mentions her name although she isn't available at the start.
That One Boss: Grunty in both Kazooie and Tooie; Weldar and Mingy Jongo in Tooie.
Rusty Bucket Bay, mainly due to the engine room, which has annoying to avoid propellers and gears. It's also all above a Bottomless Pit, and thanks to the musical notes being record-based (changed in the XBLA port), you will lose all your notes if you don't anticipate how annoying this room will be. There's also a switch Jiggy, where you need to race across all the treachery and make it to the boat's motors under a strict time limit. General consensus is that it's best to get this room over with first and then tackle the rest of the level.
Grunty Industries in Tooie. It's by far the most complex level in the entire game, even though it's only the sixth out of eight. Terrydactyland too, though mostly because of how huge it is.
They Changed It, Now It Sucks: Replacing most of Banjo's moves with vehicles in Nuts & Bolts pretty swiftly divided the fanbase. The final game has been received positively, but wasn't too successful in terms of sales. Some detractors point out there's nothing wrong with the game mechanics themselves, in fact they're rather fun, it's the fact previous Banjo-Kazooie titles have nothing in common with them.
This overlaps with They Wasted a Perfectly Good Plot, the concept of two rivals building all manner of custom vehicles and competing against each other in huge levels sounds like a great game. But not a Banjo-Kazooie game. As an original IP the concept arguably had enough merits to become its own series.
Values Dissonance: Some North Americans might take offense to Rare (a British company) designing Humba Wumba as an extremely stereotypical Native American. It's worth noting that in Nuts 'n' Bolts, made under the supervision of American Microsoft, Rare drastically changed her design to be much less stereotypical. That said it's unlikely only North Americans would think her stereotypical.
The entire FPS level in Glitter Gulch Mine could be seen as a subtle jab at union workers/immigrants working in mines during the 19th century... maybe.
Gobi, a camel who just wants to find some water and a quiet place to rest, is constantly suffering abuse from our eponymous heroes and Gruntilda's mooks for some reason or another. By the time you see him locked up and put on display in a freak attraction at an amusement park in Banjo-Tooie and see that he's grown a very large gray beard, you can't help but want to cry for his constant misfortune despite the fact that it's necessary in order to progress.
King Jingaling also counts. The poor guy loses all of his subjects thanks to a giant tank that runs over part of his kingdom (one entire family of his subjects is killed in this way) and his reward for pointing Banjo and Kazooie in the right direction and giving them a Jiggy is to be zombified.
Klungo is an unrepentant villain who makes it clear that he doesn't regret anything he did while working for Grunty, but the sheer amount of abuse she put him through makes you feel more than a little sorry for the big guy.