There's a hidden credit line in the ROMs of both Bubsy in Claws Encounters of the Furred Kind and the SNES version of Cool Spot which reads:
(C) 1992 Basement Boys Software

Basement Boys Software were a group famous for making hacking tools on the Commodore 64 in the late 80s, who had some members go on to Chip Level Designs, a company that used to provide sound programming for a number of SNES titles.

When the Japanese version's passwords are put together in a string, they make up the first 114 digits of pi.
(3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328)

The PAL and NTSC versions of the game use vowels instead of numbers, and are mostly made of random strings.

Bubsy in: Claws Encounters of the Furred Kind was censored during the process of obtaining a Nintendo Seal of Approval, with two known instances being the removal of a cartoonish beheading death animation, and a catnip hazard which resembled marijuana and was replaced with banana peels. These changes also applied to the Sega Genesis release of the game.

The password for Level 4: Fair Conditioning is "MKBRLN", short for Mike Berlyn, the creator of Bubsy.

Bubsy's catchphrase, "what could possibly go wrong?", originated as a self-deprecating catchphrase from the Claws Encounters of the Furred Kind development team when the game ran into issues. Another phrase in consideration was "Whatever blows your hair back!", which Bubsy would say in the opening to Chapter 4: Fair Conditioning in the final game.

Before settling on the artificially-sped-up voice that Bubsy would get in the final game, other accents in consideration for Bubsy were a Brooklyn accent and a Yiddish accent.

When Bubsy creator Micheal Berlyn pitched the game idea, it was initially denied, with his producer claiming "Go back to writing stories, that's all you know" (refering to Berlyn's history in text adventure games). When Berlyn asked for an option to prove his platforming know-how, they asked for him to write an analysis of Sonic the Hedgehog and why it works as a game. Berlyn would spend 10 hours a day playing Sonic in order to write an essay about the game, and Bubsy got the greenlight, though he did have to find a different producer.

Prior to the creation of Bubsy, Accolade tried to encourage Michael Berlyn to use Cheetos mascot Chester Cheetah instead of creating a new character for the game, but Berlyn convinced them by pointing out how creating a new character would be cheaper than licensing out an established mascot.

Accolade's marketing department attempted, and failed, to get Bubsy to wear pants.

In 2018, the Bubsy series fandom Amino was visited by a user named "Beelzebubsy" alleging to have unreleased concept art drawn by Ken Macklin for Bubsy's design in Bubsy in Claws Encounters of the Furred Kind. Bubsy fans immediately noticed that one design - a female Bubsy that was scrapped for being "too sexualized" - bore a close resemblance to "Modern Bubsy", a fan-made interpretation of the character as a depressed transgender prostitute created by SqrlyJack, an artist who hates Bubsy and gained notoriety for being malicious towards Bubsy fans. This connection was further drawn by the presence of another alleged prototypical design inspired by Michael Jackson, who SqrlyJack is known to be a fan of, and his jacket used in the music video to Jackson's song "Beat It", as well as a later post by the same user showing a screenshot of a Bubsy parody from one of her RPG Maker games. The third concept art does have a strong resemblance to a real piece of Bubsy concept art shown in a 1990s magazine, suggesting it may have been traced.

If one observes the hoax concept art closely, they can see that the attempt at replicating Macklin's signature does not completely match up with his real signature, such as having a lowercase a with a double-edged side instead of one, and a lowercase k without a sloped bottom, adding to the already strong suspicion that the concept art was faked.

Another Bubsy fandom member, Xindictive, who was on a Bubsy Discord server with late Bubsy creator Michael Berlyn, has said on occasion that both Berlyn and a former friend of SqrlyJack have confirmed the images to be faked for a fact. However, since the Discord server where these communications presumably took place has been closed as a result of hacking, it is hard to access these direct confirmations.

Although the modern perception of Bubsy in Claws Encounters of the Furred Kind places it as a generally mediocre-to-bad game, it initially received highly positive scores upon its release in the 1990s.

Bubsy in Fractured Furry Tales was originally intended to be a straight port of Bubsy in Claws Encounters of the Furred Kind to the Atari Jaguar, owing to the Jaguar's hardware similarities to the Sega Genesis. It was ultimately decided that, due to the age of Claws Encounters at the time, it would instead be a new game built off of the older game's engine. Accolade were not able to provide source code for Bubsy 2 due to it not having been completed at the time.