From the Super Mario Wiki, the Mario encyclopedia
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Dodgy is a positive status effect only found in Paper Mario: The Thousand-Year Door. Mario, his partners, and his enemies can all receive this status effect. A Repel Cape or Flurrie's Dodgy Fog can usually be used to get this status. When active, the recipient has a dodge rate of 50%. Appropriately enough, the symbol for the Dodgy status is a Repel Cape. Some bosses such as Macho Grubba and Sir Grodus can use magic to power themselves up with the Dodgy status. Magikoopas can use this ability too.
Related to the Dodgy effect is the random stage mist, which applies the same effect to all participants in battle. If Mario has Dodgy active while mist is on the stage, 75% of attacks will miss him.