Errors from Holly Jolly Jimmy:
Cindy and Libby "receive coal for Christmas" but they shouldn't be too disappointed because they already got lots of presents (that they opened early.) Also, in Jimmy's house there are already lots of presents around the tree before Santa comes. What, are the presents from Santa just a bonus or something? This is the only media I know where Santa actually being kids' parents and Santa Claus actually exists at the same time.
And if Jimmy had already done every country in the world (including the U.S.), how could he forget Retroville, his hometown?
Since Cindy is the smartest character besides Jimmy this episode implies that Jimmy is the only character in the entire show that should know how to use the hypercube, but in other episodes (JTPH2 for instance) other characters are seen using it with no problem.
Errors from other episodes:
In "Beach Party Mummy" Cindy should know the center of the Earth is just a bunch of hot dirt.
I'll let you know if I think of any more (There are lots!)