You always start form twinleaf town right? So go to the lake closest to twinleaf, and use surf to go to a cave in the middle of nowhere, go inside, and you'll hopefully find a mesprit. Mesprit runs away from you, so I suggest you have a Pokemon with Mean Look.
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mesprit is at the descon wold and then it will be at verity lakefront and then it will start going around sihhoh in Pokemon platinum
Mesprit moves around the world at random so it could potentially be anywhere after it runs away. To find where he is, use the map on the Poketch.
In map 22 (Ground)
You can't I don't think.
The one you need to find mesprit is called the marking map you can get one from a guy in the pokech building in jubilife city (he has brown hair ).