The security guard spends several minutes in the rain. When he goes into the lab to investigate he is dry and leaves no wet trail.
As the townsfolk drive to the lab at the end of the movie, as the guy on the scooter heads offroad, his scooter becomes a dirtbike.
When Paul picks up the toy car with the Plutonium he is kneeling on his knees in the dirt. There was just a very heavy rain storm, yet his pants are dry around the knees when he stands up.
Paul's mother is surprised when he gets up at 4:00 (although his clock reads 2:33) in the morning at the beginning of the movie. Later on, she tells Mathewson that Paul has been getting up this early - and earlier -regularly for years.
Paul's dropped rubber glove mysteriously appears on his hand as he reaches for his bag.
Plutonium must be alloyed with another metal (usually gallium) in order to prevent forming allotropes which cause it to crack while cooling. Cracks in the pit would have significant impact in the weapon, and could result in a fizzle (non-nuclear explosion.)
During the process of making the sphere of plutonium Paul doesn't use any type of protection (filter) from airborne plutonium particles. There is a high probability of death when plutonium is inhaled. As a minimum it results in radiation sickness.
A nuclear bomb with a plutonium core requires implosion "assembly" (compression of the core to start the chain reaction), and developing the precision explosive lenses to achieve that is beyond the scope of anything but an industrial-scale research and development project.
The specific details of the construction of the bomb and all its component parts are incorrect (obviously).
Every time Paul opens the glove box in Dr. Matheson's Mercedes he picks the lock with his nail file, but never locks it again. The glove box lock is simply set to lock automatically when closed.
Paul handles liquid plutonium with no protective equipment. All of the plutonium is kept behind the glass wall for a reason. The glass wall projecting the scientists in the lab would be leaded glass to protect them. Yet Paul handles the plutonium with no protection. If this were indeed plutonium, if Paul, and his girlfriend lived long enough to get home, they undoubtedly would have been dead by morning.
Paul shows Jenny a fistful of five leaf clovers that he had picked some time ago from the grounds of the lab. When revealed, they're crisp and freshly picked. If they were in his pocket for as many hours, they would have withered and been much darker in color.
So much radiation has evidently escaped the nuclear lab that Paul finds a handful of 5 leaf clovers outside. Labs are built to contain its radiation and monitored by the Nuclear Regulatory Commission for leaking radiation. If radiation were to escape to produce that so many 5 leaf clovers, it would register on sensors throughout the region, US, and international community (just as sensors Sweden detected fallout from faraway Chernobyl). Further, if enough radiation had escaped the facility to cause so much clover to mutate into 5 leaf clovers, people would also have been affected, particularly those that work at the lab. Most, if not all, would have gotten sick and some died. Further, the Federal Government would have stepped in to evacuate and cordon off the area in order to contain this all of this leaking radiation (again, much the way the Soviet, now Ukrainian, governments did with Chernobyl). But if that had happened, no movie.
After Paul mixes together his "fake" green Plutonium solution, he pours it into a bottle with a VO5 shampoo label. The bottle is a standard dish detergent bottle, not a classic (1986) styled VO5 angular bottle. Also, the topper is a standard dish detergent top, not the open top of a shampoo bottle.
The bottle had to be changed because a classic VO5 shampoo bottle is opaque.
When Jenny mentioned the members of the Nuclear club, she overlooked India who had tested a nuclear bomb 1974.