Well, I think I'll clean up some missconceptions about Bad Eggs right now.
My Pokemon Fire Red actually has 3 Bad Eggs on its save file. Here's how it works though. Let's say you enter two "encounter this pokemon" codes (I did Mew and Jirachi) and you encounter something completely different in the wild (Fearow with NO HP), I quickly throw a Master Ball at it and it's caught, I catch two more because hell, they're Fearow and they're shiney at that), now I go to the pokemon center to see what I caught and...le gasp, 3 Bad Eggs. Now, I decided to have some fun. My gameshark that I had at the time (not any more, advice kiddos, DO NOT LEND OUT GAMESHARKS) had the ability to make a direct backup of the game's Save Flash, therefore allowing me to look through the save game's data. A friend of mine pointed me in the direction of where the box I had stored my pokemon was and sure enough, I found the information about my Bad Eggs. I looked through and what I saw actually reminded me of when I disassembled Pokemon Gold and found my Glitch Eggs. In all reality, the egg was no more than an egg, but with two problems. The first problem is that it already had the immunity to Pokerus. The second problem scared me a bit, there was NO species data, so the egg could not hatch. I decided to test this by loading my file in an emulator with a backed up copy of Pokemon Fire Red that I had made, and my theory was correct. I used the Instant Hatch and of course the egg hatched, but when the screen goes white after the egg broke open, the game completely froze.
Bad Eggs are no more than Eggs with no hatch data, but if they are hatched, there is a MAJOR risk if you're using a cartridge in that the saved game can become horribly damaged.
I'm not doubting that Bad Eggs don't exist anymore, in fact they may very well still be present in Diamond, Pearl, and even the up coming Platinum and the Gold and Silver remakes. Here's pretty much my reccomendation on how to dispose of Bad Eggs.
Obtain a Pokemon Generator, I prefer Cirus Pokemon Generator, as it works for the RSE and the FR/LG games. Next, put the bad eggs in a slot, by default my generator is set to use the last box's last slot. Place the bad eggs there and save your game. Now, in the generator, make a pokemon. If you dont' want to cheat, make a cannonfodder pokemon (Ratata, Zubat, etc). Now, generate the code for your cheat device and use this code in the device. This will replace the Bad Egg with a cannonfodder pokemon. Now, you don't have to save and restart for each egg, instead what you do is you take the next bad egg, put it in said slot, then switch boxes and it'll be replaced with the cannonfodder.
I of course haven't done this to my Fire Red though because I no longer posess a Gameshark (Fucking FUCK).