7. Michael Bay - Armageddon
The Plot Hole: Why on Earth would NASA train drillers to become astronauts in order to destroy an asteroid rather than, you know, training astronauts to become drillers? Clearly one of these methods is far easier than the other.
This plot hole has been discussed at length by many, but nobody better than star Ben Affleck, who in the film's DVD commentary explained that he raised the issue to director Michael Bay, who promptly told him to "shut the f*** up."
In fact, Affleck goes on to quite openly tear the whole movie a new one in the commentary, while making it abundantly clear that Bay was well aware of the movie's logic-defying issues but simply didn't care.
Bay eventually even apologised for the end product, saying, "I will apologise for Armageddon, because we had to do the whole movie in 16 weeks...It was a massive undertaking. That was not fair to the movie. I would redo the entire third act if I could. But the studio literally took the movie away from us. It was terrible."
Between Bay's lack of giving a damn and some clear executive meddling, there's nothing surprising about the movie's utter lack of coherence. That doesn't stop it being goofy fun, though.