Plot hole: When Buckaroo is speaking with the president via video call (with John Parker by Buckaroo's side), New Jersey is explaining the reason humans can't see the aliens from planet 10, is a result of bacteria produced by the aliens which is then absorbed by humans via their olfactory senses, affecting their cerebral cortex. If this is the case, why doesn't the president see John Parker in his true alien persona. He can't smell him through the television. (01:04:50 - 01:05:40)
Plot hole: Chelsea says that when her deceased father gave her one of his paintings (now missing), he wrote an inscription to her on the back. She says she cannot prove that he actually did this other than he noted it in his journal and she does not know where the journal is. However, when Chelsea's father presented the painting to her on her 8th birthday, there were at least 100 adults present at her party who witnessed him giving her the painting, writing the inscription, and signing his name on the back of the canvas which was displayed to the guests. Any number of these people could be contacted and corroborate her claim.
Plot hole: The whole premise of the movie makes zero sense. Spence finds out that a certain race is rigged, but he is caught eavesdropping, so the goons are after him. They don't catch him and then the day after they stalk the betting counter looking for him. He then enlists the help of his friend Dennis to distract the goons so he can place the bet. But the villains are completely unaware about Dennis' existence! He could simply walk in and do the bet himself. He even is the guy with the money. No reason at all is given why Dennis does not place the bet himself, cash in, and walk away. Other than the fact that the movie would be done in 20 minutes and with not much of a payoff.
Plot hole: Georges repeatedly tells immigration officers about his Africa trips. This overlooks that fact that INS would have or request a copy of his passport to process his case. In real life, INS would have realised immediately that the Africa story was not real: no entry/departure stamps in his passport.
Plot hole: The Thorwalds were supposed to be in the apartment for only six months according to the lease, their phone number wouldn't have been published in the phone book for such a short lease.
Plot hole: When major Singleton challenges Brant Royle to a duel with single shot pitons, he fires one pistol, and leaves the other pistol on the bar. He then goes into his carriage and shoots himself. He only has the pistol that has already been fired.
Plot hole: Viola convinces her mother she is staying at her father's house for two weeks, but who covers for Viola with school administrators? As far as we see in the movie, Viola is not reported absent from either Cornwall or Illyria (a transfer would explain not being reported absent from Cornwall). Administrators or class mates at Cornwall would find it strange that she stopped showing up, since soccer training had already started. It is unlikely Viola officially transferred to Illyria, since her parents would have to sign off on that, or at least start paying her tuition to a different school. Viola could have called in sick to either Cornwall or Illyria, but this is never addressed in the movie. And if the soccer program at either school started before the official school year, it would make no sense for them to have a biology class with students not enrolled in athletic programs at Illyria.
Plot hole: It makes no sense that Martin would be getting the invitation to the reunion mailed to his office (or to anywhere else.) He's had zero contact with the alumni committee, and they're not going to hire a private detective to find him. He also doesn't have contact with anyone else from his hometown who might have forwarded it; his father's dead, and his mother's not in her right mind. There's no explanation for why it would have ended up there except for needing to set the plot in motion.
Plot hole: After Eli's guardian is hospitalised for acid-burning his face, Eli hears on the radio that they can't ID him because of his facial wounds. When we see him in the hospital however, only half his face is injured, the other half is fine which would make a mirror composite easy for lab techs.
Plot hole: The plot that a piece of the Roman spear that pierced Christ ends up in a hidden Mayan temple in the Amazon (which is nevertheless still full of gold etc.) makes no sense.
Plot hole: Kate could not get Leo's photo in order to get his passport.
Suggested correction: He was rich and famous, they had no problem finding information about him online, so could have found a suitable photo online (photoshopping it if needed).
Plot hole: After the incident in Chemistry class, Adam was taken to the hospital where he was diagnosed with schizophrenia. Next, Adam found out that he was expelled from school. What happened during Chemistry class was attributed to Adam's "first psychotic break" - which would fall under a medical condition for which Adam could not have prevented or controlled. The Department Of Education has laws protecting students like Adam (Individuals with Disabilities Education Act or IDEA, enacted in 1975), and the school is required to meet the child's / student's needs. An Individual Education Program (IEP) should have been prepared for Adam by his school, so the expulsion served to further the plot. (00:06:00 - 00:06:30)