How the Mew Trick Works
If you're not a geek, you don't wank to read this.
When you use Fly to get away from the Gambler, the game somehow "remembers" that a battle is supposed to be taking place on Route 8. This is what causes your Start button to stop working. The rest of the trick hinges on a twelve-byte section of memory, starting at memory location CD22 in Yellow (CD23 in Red/Blue), which contains the stats of the last Pokémon you fought. After you battle the Youngster, it will have these hexadecimal values:
8E 11 00 3C 00 1E 00 1D 00 1C 00 15
The first byte (8E) seems to be the same for all battles.
The second byte (11) is the enemy's level (17 in decimal).
The next ten bytes are the enemy's stats (HP/Attack/Defense/Speed/Special). Each stat takes up two bytes.
Additionally, this section of memory is surrounded by eight bytes on each side, which all have the value 07.
The last byte (15) in Yellow memory location CD2D (CD2E in Red/Blue) is the important one. It is the "least significant byte" of the enemy Pokémon's Special stat; in this case, it means that the enemy has a Special of 21 in standard decimal notation.
When you return to Route 8, the game tries to resume the battle that was interrupted before. For reasons unknown, it borrows byte CD2D to use as the species identifier for the enemy Pokémon, and the next byte to use as its level. If the last battle you fought was with the Youngster, these bytes will be 15 and 07. Since Mew's hexadecimal identifier is 15, you will fight a Level 7 Mew.