Oppenheimer passes a 1980's subcompact car on a side street when he's driving from Jean's to the train station. A modern pickup truck is also briefly in the background during the parade to celebrate Germany's defeat.
At the end in the movie, right before the countdown for the trinity test shot, the man with sun tan lotion on his face puts his goggles on. In the next shot, about 3 seconds later, his goggles are around his neck.
General Groves and Oppenheimer have been standing in the rain talking then they get in a car and are driven a short way and get out and are seen to be completely dry and Oppenheimer is now hatless and the ground is completely dry.
At the beginning of the movie, when General Groves is slicing the Pentagon cake, there are no flags on it. But in the next scene when his aide is walking with him down the hallway, there is an obvious miniature flag on the piece the aide is carrying.
General Groves (Paul Newman) is a one star general but towards the end of the film as he's driven away the plate on the back of his car shows 2 stars. However, by that time historically, he was entitled to wear two stars.
It was actually Seth Neddermeyer who originally conceived the implosion theory, and John von Neumann who refined it to usability.
The sequence of the Trinity explosion is reflected on one of the scientists. We see 1] a reflection of an initial explosion, then we see a 2] large wind blast flapping his cheeks, then finally 3] we see the reflection of the mushroom cloud. In actuality the blast wave took about 40 seconds - much longer than the 2-3 seconds in the movie - to travel (and it does not go through leaded glass).
General officers do not wear branch insignia. All the general officers in this film do.
The Navajo train only ran until January 14, 1940. Also, it carried no diner west of Kansas City.
The telegram to Oppenheimer states that Dr. Jean Tatlock committed suicide 5 January 1945. She actually committed suicide a year earlier, in January 1944.
When General Grove's plane is turning around in the hanger near the end of the movie there is an "N" number on the tail. "N" numbers are present day registration numbers of private aircraft. There were no "N" numbers on World War II military aircraft.
Before boarding the plane near the end of the movie, the back window of the car Gen. Groves is riding in can be seen flapping in the breeze as it's made of thin plastic sheet instead of glass.
Many of the Jeeps used in the film are postwar versions.
In the first shot of the experiment that Michael Merriman is performing, with the two hemispheres of beryllium surrounding a core of plutonium held slightly apart, he measures the gap between the hemispheres with a dial caliper - but the dial caliper was not developed until after the war.
Many of the male actors have 1980's blow dry hairstyles not period to the 1940's.
As J. Robert Oppenheimer walks with General Leslie Groves in the rain at the Trinity atomic bomb test site, he tries to convince the general to call a halt to testing the atomic bomb as "...with the wind and the rain we could send radioactive junk all the way to Amarillo!" As Oppenheimer says these words, the general begins to speak to the New York reporter to get him to write three reports based on what are believed to be the potential results of the bomb test. Immediately after the general tells the reporter "I want three reports," we see Oppenheimer continuing to shout words, apparently in protest, to the general. We never hear Oppenheimer's words, however, as they have been completely edited out.
At the party, Dr. Schoenfield (John C. McGinley) is wearing his Captain's bars 90 Degrees off. They should be parallel to the lower edge of the shirt collar not the edge that touches his neck, as is shown.
The Battle of the Philippines ended on 8 May 1942, with the Allied surrender of the Philippines to Japan. By that point, US soldiers stationed in the Philippines were either evacuated off the islands, POWs in a Japanese prison camps, missing in action, or killed in action. Nearly a year later, in April 1943, John Cusack's character, Michael Merriman, arrives in Los Alamos. Shortly afterwards, he writes to his Dad that "I think of Jimmy, fighting in the Philippines". Later, when he mets Laura Dern's character, Nurse Kathleen Robinson, he explains that he has a brother, who "is a solider". By April 1943, it seems unlikely that Merriman would call his brother Jimmy "a solider" if he were a POW, missing in action, or dead. If Merriman's brother had been evacuated off the Philippines, it is unlikely that Merriman would say Jimmy is "fighting in the Philippines", rather than the past tense, or saying that he is now fighting a different battle, or "fighting the Pacific" or "fighting against the Japanese", etc.