Christmas Special: Part 2 - S3-E2
Plot hole: Lee and Dawn overstay their tourist visa in the US, then fly back to the UK for the Office Christmas party. They then get into a taxi to go out to the airport in order to return to the US. They're kidding themselves. As I know (to my cost) when you overstay a tourist visa, the US Immigration Service finds out when you check in at the airport on departure. They'll be refused reentry, and probably barred from entering the US for up to six years. (I got a three year ban.) Neither Lee nor Dawn could possibly be unaware of this nor think they could beat the system as they would have been arrested when they checked in in Florida on departure (as I was), and they would have remained in small holding cells until the paperwork banning their return had been processed and their passports stamped 'Invalid for U.S. Entry', as mine was. (All this takes about seventy two hours, so they'd have missed the Christmas party anyway.) The mistake is NOT that they were able to leave the USA - that is explained (it's still not possible, but in the context of the show and the suspension of disbelief we are meant to believe it) the mistake is that they are on the way back to the airport to return. That's absurd. They would have been under no illusions as to their banned status re reentry to the USA.
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."
Plot hole: Season 5, episode 20 (My Lunch). One of Dr. Cox' patients needs a heart valve transplanted. Heart valves don't have to be transplanted from another person. They can be replaced by a metal valve, or the surgeon can create a new valve from a different part of the patient's body. There was no reason to wait for a donor valve when they had other options available.
Plot hole: When Lizzie and Gordo are sitting at lunch, Gordo says that he doesn't like broccoli (referring to the pile on his plate) and that he tries to avoid it. However it is established in many scenes that Lizzie's school has a self serve cafeteria, so why does he have broccoli? (00:56:45)
Oops!...I Did It Again - S2-E22
Plot hole: Lily was vomiting because of the antibiotics she was taking for the infected tattoo. But initially, Sean and Claudia were both puzzled by her being sick. As a teenager, how could she have seen a doctor and been prescribed medicine without a parent knowing?