Copy Protection: Pirate copies of the cartridge obviously do not have the lock-on slot. This means a huge chunk of content will be unavailable, so even though the game is still fully playable, it's a lot less interesting.
Manual Misprint: A few of the enemies from Sonic & Knuckles showed up in Sonic the Hedgehog 3's instruction manual.
Screwed by the Lawyers: According to Cirocco Jones (mistakenly credited as Scirocco in the Sonic 3 credits), there's a huge legal mess concerning the music used in the games, likely due to unpaid royalties, improperly crediting the musicians, or (as was the case with Dreams Come true), licensing issues. Considering that two of the music composers (Michael Jackson and Brad Buxer) directly sampled songs from their respective discographies, the latter is the most likely. Some believe this is the reason why a Taxman/Stealth remaster seems unlikely, as Sega has only been able to release direct emulations of the original game or recoded versions with different music (as seen in the PC version).
There tends to be confusion as to why the original Sonic the Hedgehog could not be locked in with Sonic & Knuckles. The two most popular explanations are Knuckles would have dramatically altered the color pallet or that Knuckles gliding on conveyor belts in Scrap Brain Zone would cause the game to crash. Both of which were solved by the famous rom hack Knuckles in Sonic the Hedgehog 1.
Despite what your third grade friends (and basic logic) told you, it's not possible to beat the Fire Breath the first time you see it and stop it from burning Angel Island. No matter how fast you hit it, it'll successfully set off the firebombs and escape with its robotic life.