Okay, I know most of these aren't 'lost' now that Sonic & Knuckles is out, but the hangovers from Sonic 3 (and its manual) are still there! Segments of the Sonic & Knuckles code are actually in the basic Sonic 3 ROM, waiting to be activated!

Firstly, on the level select it shows two Sonic & Knuckles levels (Mushroom Valley and Flying Battery). However, it won't let you play them. I think these levels were originally intended to be in the basic Sonic 3 cartridge, but were taken out at the last minute, hence the level select names. Rumor has it that the Japanese version of Sonic 3 actually DOES feature these zones!

Secondly, the manual lists two badniks that don't feature in the levels at all.

The 'Technosqueek" badnik (left) only appears in the Flying Battery zone in S&K. The "Corkey" badnik (right) only appears in Sonic 3D!

UPDATE: The 'Corkey' badnik DOES actually appear in Sonic 3, it's just not easily visible. In Launch Base Zone, there are some bars and from those bars the Corkey enemy hangs shooting a laser down on top of you. Thanks to Miles Prower for the information!

Flying Battery is actually in a half-complete state in Sonic 3. (A bit like the unfinished Hidden Palace). Using my Action Replay, I was once able to access the badniks of Flying Battery, and put them into Angel Island, although the graphics weren't complete. I noticed one that seemed to fire out two shells constantly, and one that kept looking around and running to the other side of the screen. When I got S&K, I discovered that the 'running around' one was actually the TechnoSqueek, and the one that was firing out two shells was the Blaster, both of which appear in Flying Battery.

Another thing I was able to do with my Action Replay when I first got Sonic 3 was to access Knuckles in the character select screen, and play him in the levels. Er, sort-of. Although you get to see the pink echidna on the select screen, you still get Sonic as an in-game sprite! However, the character responds to Knuckles stats (lower jumping, better braking and an overall slower top speed). When you complete a level, you get the message "KNUCKLES GOT THROUGH ACT ONE".

You get to see Knuckles on the character select screen...

But you still get Sonic as a sprite!
Also, the game says KNUCKLES instead of Sonic on the 'got through' screens. (Notice the end panel)

An incomplete version of Lava Reef.

In Sonic 3, the Flying Battery badniks move around as they should (although the graphics are not implemented).

Just like in the completed Flying Battery

What I also noticed is that all the S&K music is already in the basic Sonic 3 cartridge, and can be played from the sound test! Some S&K music even makes an appearance in normal Sonic 3 levels! For example, on the boss of Hydrocity act 1, stay underwater until the countdown begins. Then, when you jump out you have S+K music for the boss!

Finally, here are some savestates for Sonic 3:

SONIC3.GS1 - Level select and debug enabled from the title screen - select Sound Test
SONIC3.GS2 - Knuckles selected in the File Select screen
SONIC3.GS3 - Incomplete playable FBZ. You can place the badniks with debug, and they will have correct graphics.