Trainer-GAF: I have a small request. I've calculated it should be possible for a Pokémon to grow by 59 levels in a single battle; anyone want to test? I can't do it myself yet, as I haven't beaten the game.
Step 1: Get a level 1 Pokémon with a
Fast growth rate, traded from a different-language game (internationally-traded Pokémon gain a little more Exp. points), and give it the Lucky Egg.
Step 2: Wait until a Doctor/Nurse trainer shows up in one of the Nimbasa City sports stadiums.
Step 3: Use the Entralink to get an Experience Power ↑↑↑, S, or MAX.
Step 4: Battle the trainer (they should use a level 65 Audino), and win by switching and using Explosion (so the level 1 gains all the Exp. points). Alternatively, use a Ghost-type level 1 (Misdreavus, Shuppet, Duskull) and beat it with Toxic.
This should result in the level 1 gaining 178632 Exp. points and growing to level 60. Fun stuff.
Speaking of huge level gains, I left a Munna in the Day Care when I first reached it. I checked back once I got to Mistralton City. 'Your Pokémon is doing fine. Its level has increased by 42'. Munna is now my highest-level Pokémon