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I just wanted to point out that Jim never had the wand in the first place. The wand belongs to Guido. Lisa used it to turn herself back into Jerry, and then used it to become invisible, before leaving and taking the wand with him. Jim never once held or used the wand.
But after seeing what it could do, Jim now desires to have the wand for himself. At least, that's what I was imagining in my head.
Okay, I figured out a plausible way to fix it. Given enough time, I can figure out a way to fix almost any continuity error.