The Goblet of Fire's Biggest Plot Hole Has a Very Reasonable Explanation
It always bugged us that there was no actual investigation after the Goblet of Fire spat the name of an underage student to be the fourth Champion. Weird, isn't it?..
The entire storyline of Harry Potter and the Goblet of Fire is based on what appears to be one huge plot hole: no one was interested in investigating the malfunction of the Goblet of Fire.
The ancient artifact chose the fourth contestant against the rules of an international tournament, and the "extra" Champion is underage.
Somehow, everyone just decided to roll with that and act as if nothing happened: the rules were forgotten, the extra equipment brought in, and the Tournament went on.
No official investigation was opened despite officials from three countries involved.
No real attempts at stopping the Tournament were made, apart from the weak arguments from Madame Maxime and Igor Karkaroff at the start that were immediately forgotten. No Ministry intervention happened whatsoever.
This looks like a massive plot hole, and we've considered it such for the longest time until it dawned on us: there's a very reasonable explanation for such a reaction!
The incident happened on British soil, at the British school.
The actions were expected to be taken by the Ministry and Hogwarts representatives, but they had no reason to interfere. Why is that? Let's take a closer look at who they were.
Albus Dumbledore was the Headmaster of Hogwarts, and he didn't need to interfere. He could've suspected the Death Eaters' involvement, but allowing the events to unfold was crucial to figuring out the people behind them.
Also, the Tournament was a perfect set-up for him as the dangers of the Trials were completely controlled.
Keeping a close eye on what was going on with the Tournament allowed the Headmaster to stay in control for the longest time, and he was almost right to do so.
Barty Crouch Sr. was the Head of the Department of International Magical Cooperation, the key person in the Tournament, and the main representative of the British Ministry of Magic. Barty had all the reasons to interfere…
If not for one tiny little detail: he was under the Imperius curse that entire time and followed orders.
His son, Barty Crouch Jr., was the puppet master, and it's unlikely he only seized control over his father. While pretending to be Alastor Moody, he had access to oh so many places and oh so many people; it's only natural that he used said access to make even more decision-makers hush up the potential scandal.
Now, the entire web is completely dependent on Dumbledore and the collective Crouch. Neither of them is interested in an active investigation, and both of them have immense influence and power.
The representatives of the two international schools can't do anything: their students are magically obliged to participate, and the Headmasters themselves don't have a rule over anything in Britain.
The public trusts the Headmaster of Hogwarts and the best ex-Auror in the country. After the initial backlash, the people calmed down, convinced that the situation was under control.
The Tournament goes on as the magical contract's ties can't be broken anyway. Very soon, everyone's used to the fact that there are four Champions.
Art definitely imitates life on this one, let us tell you this much.