Pokemon Brilliant Diamond & Shining Pearl haven't even been out a week yet, but that hasn't stopped people from uncovering all manner of bugs and glitches. Although the games are pretty polished overall, there are still some fun mistakes that have been included in those cartridges.
Let's start at the beginning. Everyone knows the first few hours of a Pokemon game are a slog - it's all tutorials and Normal-type moves. Well, this glitch allows you to skip over the introductory parts of the game. You can position your rival and talk to them so you can get over a ledge and head off to Sandgem Town before you even have a starter 'mon.
Movement has been freed from Diamond & Pearl's four directions, and you can now walk in any direction you want. This has led to some interesting glitches in the Snowpoint gym. If you slowly walk off one of the snow tiles, you can get caught in the bottom of the gym, meaning you'll need to reset to escape. You can also skip the entire gym puzzle and trainers by simply walking into a slope next to Candice's stairs.
There's a Surf glitch that allows players to Surf on land, leading to them being able to access out-of-bounds areas and encounter legendaries such as Giratina and Shaymin way earlier than planned. You have to mash 'A' by a body of water as a trainer battle is about to start. The game saves the Surf input and pops you on a Bibarrel once the battle is over.
This glitch has been iterated multiple times already. You can change the height you're Surfing at - allowing you to access different areas - by opening the ball capsule menu, previewing a capsule, and exiting again.
One glitch that isn't very fun or useful has also been found. When shiny hunting using the PokéRadar, the shiny patch of grass can appear under an NPC, making it impossible to walk on and thus losing your encounter. So shiny hunt in patches of grass without NPCs if possible.
Perhaps the funniest glitch is one that makes trainers attack Pokemon. If move animations have been disabled, then moves like Dig and Fly which cause Pokemon to disappear for a turn will make it appear as though the trainer is attacking. Trainers are programmed to do an animation when their Pokemon attack, so this crossover makes it look as though an Infernape is getting kicked in the head by a human.
If you want to see more of these glitches, check out Eclipse_tt's thread of them. They're adding new ones as they're discovered.
It has also been discovered that the calculator on the Poketch is completely busted. Not really a glitch, but it's quite funny nonetheless. It appears to absolutely hate fractions - as did most of us when we were kids. There's also a cloning glitch that's relatively easy to perform - check it out before it gets patched.