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Inverted sprites (also known as Scrambled sprites or Reversed sprites) is a side-effect of encountering certain Glitch Pokémon.
When one first enters the battle, the trainer sprite is "glitchy" in appearance. It is also partially reversed from its normal state:
After the battle starts, one's Pokémon also have the "glitchy" back sprites. Note also that the enemy Rattata
also has its sprite reversed:
Once one uses an attack, the enemy Pokémon's sprite breaks as well.
As the name would imply, having inverted sprites causes sprites to appear backwards or flipped. This x-mirroring effect is used in the stats screen normally, but is only intended for front sprites and does not react well with other things. For instance, the trainer sprite and back sprites get a "Glitchy" appearance when flipping is attempted. In addition, while the front sprites flip properly originally, once the sprite is updated (through attacking), it breaks. The effect causes no permanent damage on the game.
To fix the effect, one needs to view the Pokédex entry or stats screen of any non-glitch Pokémon.
Official Nintendo statement
Nintendo has an official description of Missingno. listed in their Customer Service troubleshooting section, which includes a nonworking method of fixing the effect:
"MissingNO is a programming quirk, and not a real part of the game. When you get this, your game can perform strangely, and the graphics will often become scrambled. The MissingNO Pokémon is most often found after you perform the Fight Safari Zone Pokémon trick.
To fix the scrambled graphics, try releasing the MissingNo Pokémon. If the problem persists, the only solution is to re-start your game. This means erasing your current game and starting a brand new one." 
Nintendo was incorrect on the method for fixing this behaviour; releasing Missingno. does not fix inverted sprites. Instead, looking at the stats of a non-glitch Pokémon should fix the problem.
- ↑ Nintendo - Consumer Service