During Shadow's story, you can hear the voice actor for the G.U.N. soldier flub his line and repeat it again... and it's all unedited. Also, another G.U.N. soldier over Rouge's radio refers to the Scepter of Darkness as the "Book of Darkness" at one point, though the subtitles are correct.
The very first quest in the game is called "The winder of a shoemaker". It's definitely a typo, and was probably supposed to be "wonder".
Christmas Rushed: After Yuji Naka left Sega, Sonic Team was given until Christmas to release the game for the franchise's 15th anniversary.
Creator Killer: A handful of Sega employees, including two of the game's three story writers, were fired from the company after Sonic 06. In addition, Shun Nakamura, who was one of the leaders of the project and one of those story writers, became less involved with the Sonic franchise as a whole, and the controversy did not do Yojiro Ogawa and Yuji Naka (the latter of whom had departed Sega by this point) any favors for their careers; Takashi Iizuka was eventually put in charge of Sonic Team at the end of the decade to try and fix their mess.
Development Hell: A major reason for the game's lack of quality. The game's original director, Yojiro Ogawa, split the team up, and personally oversaw the team in charge of the Wii port. However, Ogawa decided that porting 06 to the Wii wasn't worth it, and decided that his team would make Secret Rings instead. He then abandoned 06 entirely, leaving it in the hands of Shun Nakamura, and taking his part of the team with him. Later, Yuji Naka left to start his own studio, Prope, downsizing the team again.
A variation: when they reconvened to do Sonic Unleashed, Pokecapn's band usually referred to this game as "that other game" whenever the subject came up. Not surprising considering the effect "that other game" had on their sanity...
"NO! Shut up! Shut the fuck up right now! We vowed never to speak of that whole ordeal..."
They also refer to the magma-lizard enemies as "Dodongos" or "Thriller lizards" (after the funny dance they do when Silver telekinetically picks them up) and the flying magma enemies are "Fire Keese", after the flaming bat enemies in the Legend of Zelda, in keeping with Medibot's need to make everything fit into some other game's logic.
They dub the Demonic Spider black hole things from End Of The World "Time Dimensions".
They also give Sonic the name Rockman Classic/Rockman Blue, Shadow the name Rockman Charcoal, and Silver the name Rockman Steel / Rockman Chrome.
Mephiles is referred to as Mephistophiles, Satan, or Mephisto.
Referring to Silver's Psychokinesis as "Physics". As a result of their Sanity Slippage they use the word "physics" as a verb.
"My rings! They're getting physics'd!"
Franchise Killer: The low sales and negative reception killed off the Adventure-canon. Future games in the series would distance themselves from the canon and be either more stand-alone, or rooted to the original Genesis-canon.
Keep Circulating the Tapes: While used copies aren't too difficult to find, Sega pulled all new copies from store shelves in 2010, so don't expect a rerelease in any form.
There's also a playthrough by HellfireComms with NTom64 and Fastest Thing Alive, and as if they didn't sit through enough torture, they've begun anew, with The Helldragon replacing Fastest Thing Alive.
Later on, Some Call Me Johnny from BrainScratch Commentaries and ClementJ642 revisited the game on their own channels. The former went through a solo commentary of a pre-recorded playthrough with loading screens mostly edited out on his SGBLikesToPlay channel. The latter really didn't want to make a LP of it as a part of his Sonic retrospective, so he went for a giant 7-part review instead.
Frequent Retsupurae guest TieTuesday did his own playthrough of the game in 2017, with slowbeef popping in during the stream a few times. Tie became so fascinated by how buggy and broken Sonic 06 is, that after he finished the game, he started speedrunning it! After learning several of the speedrunning community's (yes, there is one for this game) tricks, he was able to get through Sonic's story in a little over an hour!
Medal of Dishonor: Meta-example; the game won the "Worst Game of the Decade" award over Big Rigs: Over the Road Racing, and while X-Play had ripped apart a few Sonic games prior and made their disdain for the franchise at the time known previously, this was the first Sonic game to get one of their "Golden Mullets", their version of the Golden Raspberry Award that was taken from Aquaman (the first game on the show to get a 1 out of 5 score).
Milestone Celebration: It was intended as a celebration of 15 years of Sonic the Hedgehog. One of the rare cases where such a thing went terribly wrong, due to the game being rushed to ensure it was finished in time.
ZigZagged. SEGA fired the game's writers, apologized on its multiple issues, and later pulled it from stores entirely. All as an effort to forget that the game existed, and to hope that this problem never happens within the series again. However they weren't quite ashamed enough to write it out of Sonic canon forever, as several elements from this game appeared in later installments. Silver appears in a few later games like Sonic Rivals and one of the levels with a boss fight are in Sonic Generations, albeit with a major gameplay overhaul.
During the 25th anniversary event, all the Sonic games up to that point were listed and each game was given a cheerful description. When the list got to Sonic '06 its description was just the game's loading screening.
Sonic makes reference to the game in LEGO Dimensions, and makes it clear he'd rather forget about it.
Sonic:Lumpy Space Princess, huh? Last time I met a princess, Ió We... Y'know, I d— I don't quite remember. Never mind.
Early trailers and demonstration videos promised things like a day/night system, multiplayer minigames, and a "free mode" that allowed you to play as any character without storyline constraints. Several functions described in the manual are not actually in the game, including things like the implementation of the Action gauge (it is completely pointless for Sonic and is rather barebones for Shadow and Silver), "maturity" levels for Sonic's custom actions (there are none), and a flight gauge for Omega's hover (he can hover forever, there is no gauge). Most depressingly, code was found for a purchaseable gem that allowed Sonic to relive his glory days of going Super Sonic in-level, rather than just for the final boss. Such a thing was never used until Sonic Colors.
A more minor standpoint, but it was implied in some unused quotes in the game that Sonic/Shadow gets sucked into the tornado in Crisis City and the other one has to rescue them, the two nearly thanking each other. In other words, it was implied they were going to be playable in each other's action stages.