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I recently bought a copy of Blue version and have been playing around with the mew glitch to get Pokemon like lapras, gengar etc. But I am really intrigued to know why this glitch occurs. I have heard that it has something to do with the special stat. Could I use this to my advantage to catch Pokemon not found in Blue?

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You can get any (Gen 1) Pokemon you want. What I know is the special stat of the trainer's Pokemon becomes the index number of the Pokemon you get.
There's actually a very similar glitch involving Ditto, if you defeat a wild Ditto that's transformed into a pokemon with a certain special stat, you can get any pokemon you want, really. It's very handy and makes completing the pokedex a joke.
I just realized that you're a Missingno. Aren't you supposed to know all the technical stuff?

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When you perform the glitch, and fly away, the game remembers your battle, so the START button not working is due to this. The game saves a value in a 12 byte of memory, starting at CD23 in Blue and Red Version. Let's say you battle the trainer with level 17 slowpoke near the nugget bridge. This memory section works like this.

8E 11 00 3C 00 1E 00 1D 00 1C 00 15

  • 8E is the same for all battles.

  • 11 is the enemies level, (17 in decimal)

  • The next ten bytes are the stats of the Pokemon. Each one takes up 2 bytes. (HP/Attack/Defense/Speed/Special)

  • They are wrapped (in a sense) with the byte 07 on each side.

The memory section "15" is what's important (mostly) here. In standard decimal notation, this means the enemy Pokemon has 21 Special.

When you return to the route you warped away from, the game tries to resume the battle, for reasons unknown, the game takes the previously listed section of memory as a indicator of the Pokemon, and the next (07) to use as the level. Mew's hexadecimal value is 15, so the last byte (the special) is used to call the Pokemon, and the wrapped up (07) byte calls the level, so you get a level 7 mew.

Other shenanigans

  • Using growl, for some odd reason, lowers the byte wrapped around the memory address, so you can obtain level 1 Pokemon in gen 1! Which break the game in their own special way.

  • Check the hexadecimal values for all Pokemon, as these are quite useful.

  • Using ditto, you can alter the special stat to your own liking, meaning, every Pokemon in Red/Blue can be caught with this method. Stock up on them master balls and get catching.

  • You can even fight trainers, like a glitched agatha fight and Prof. Oak, who has no glitches in his fight whatsoever, which indicates he was planned but alter scrapped.

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Thanks for the in-depth answer, but where do you learn all these hexadecimal stuff?
Mainly from websites like glitchcity and just general hexadecimal courses and such. I actually learnt about it so I could find out more about Gen 1. There is a list on Bulbapedia that shows all the values of each gen 1 and glitched Pokemon, so check that out. I hope this was helpful to you.