Father Time! / Apartnership! - S1-E4
Plot hole: Timmy uses his heat vision, that he previously wished for, to win the race for his future dad. But it's revealed later in "Smarty Pants" that if you use a previous wish in a contest, it is magically taken away because it's cheating.
Suggested correction: That is true, that rule was mentioned in a later episode. However in the episode Christmas Every Day, it was revealed that new rules could be added at anytime. So it's possible that the rule simply didn't exist yet. Although, this plot hole may apply to any episode released after "Smarty Pants."
Father Time! / Apartnership! - S1-E4
Continuity mistake: When an 'angry' Wanda throws a styrofoam picture of Cosmo and Wanda on the floor near Cosmo, it breaks, but some shot later, both pieces are gone.
Chin Up! / Dog's Day Afternoon! - S1-E5
Continuity mistake: When Cosmo and Wanda are saying what Vicky likes more than Timmy, their castle brick outline changes.
Chin Up! / Dog's Day Afternoon! - S1-E5
Continuity mistake: This mistake is found in the episode where Timmy wishes himself into the Crimson Chin's comic book after causing the Crimson Chin to become depressed. After defeating the Bronze Kneecap, the Crimson Chin are walking, and the Crimson Chin has no cape. When they appear before a large American flag, the Crimson Chin suddenly has a long, flowing, red cape flapping in the win. When they walk into the "letters to the editor" page, the Crimson Chin no longer has a cape.
Chin Up! / Dog's Day Afternoon! - S1-E5
Deliberate mistake: When Cleft (Timmy) and the Chin go to the last page with the letters and they get to Timmy's letter, Chin says he spelled Chin wrong yet you must see it's spelled right.