I have lots of info to put on that if you want.
About the Zapdos speed showed by _Crystal, its not a NB glitch, but a GB glitch.
Here's a complete view on the Paralysis Status:
If a Pokémon is affected with the Status Paralysis, it will lose 1/4 of its Speed Stat. Also, before it use any move, it will have 1/4 chance of not attacking on that turn.
If a Pokemon with Status Paralysis use Baton Pass, the selected Pokemon to get on the field will not have its speed altered, even if its with Paralysis too. This means that if you use Baton Pass to switch to a Pokémon with Paralysis status, even if you do not pass any stat modification, the Pokemon will take maintained its original speed.
However, if the Pokemon suffer any stage modifier effect on his Speed, the game will recalculate the speed of the Pokemon, and its speed will again be reduced by 1/4.
If the battle is doing at Pokemon Stadium 2, and if a Pokemon with Paralysis Status use Baton Pass to another Pokémon with Paralysis, two situations must be considered:
1) If you passed any speed stage increaser (Agility comes to mind), the Pokemons speed will be reduced by 1/4.
2) If you don't, the new Pokemons speed will not be reduced, EVEN if it is affected by any speed stage modifier after that (the game recalculates the speed, but ignores the Paralysis effect of reducing the speed).
Sorry for any grammar errors, my english isn't very good.