Continuity mistake: Near the end of the movie, when Oppenheimer is being interrogated in the small room, his lawyer is on the phone (we later find out it's Kitty). In a wide shot, he gives Oppenheimer the phone, and he puts it to his left ear. The next shot is a tight shot of Oppenheimer's face with the phone to his right ear.
Continuity mistake: The strong wind blowing when Oppenheimer is approaching/climbing the tower completely stops when he's at the top.
Continuity mistake: When the scientists are testing the plutonium in the desert, there is a shot of Oppenheimer and Groves walking over to the explosion site. In the background, Lilli Hornig can be seen climbing over a small dirt hill. When the shot cuts, Lilli can now be seen standing next to George Kistiakowsky closer to the explosion site. When the shot cuts back to Oppenheimer and Groves, she is still climbing over the dirt hill. (01:36:50)
Continuity mistake: When Lawrence enters the classroom, where he finds Oppenheimer writing "F.A.E.C.T." on the chalkboard, the letters C and T are written differently in two distinct shots. (00:36:02)
Continuity mistake: When Roger Robb has finished questioning Oppenheimer for the final time, in the shot of Robb saying "Just as it had with the atomic bomb, exactly," he has no glasses on. When the shot cuts, he suddenly has glasses on. (02:46:28)
Continuity mistake: When Roger Robb asks Kitty if there are two types of communists, Kitty says she couldn't answer that one, to which Ward Evans replies, "I couldn't either." Gordon Gray can then be seen turning his head to face Evans, but when the shot cuts to focus on Evans, Gray is looking straight forward at Kitty. (02:40:55)
Continuity mistake: William Borden is handed a letter that he wrote to J. Edgar Hoover. A copy of the letter is then handed to the other people in the boardroom. In a shot focusing on Borden, the letter is on the table, but when the shot cuts, he is suddenly holding the letter. (02:30:12)
Continuity mistake: When Roger Robb asks Oppenheimer if Haakon Chevalier still his friend, Oppenheimer replies "Yes," and then it cuts to Lloyd Garrison, unhappy that he said that. In this shot, Garrison's forearms are on the table, but when the shot cuts, his forearms are on his lap. (02:26:50)
Continuity mistake: Oppenheimer comes across a paper for a discussion on "The Impact of the Gadget on Civilization" among the Los Alamos scientists. In the shot of him grabbing the paper, it is soaking wet, but in a close-up of the paper, it is nearly dry. (01:34:35)
Continuity mistake: After speaking with Niels at the Christmas party, a woman approaches Oppenheimer about a call from San Francisco. In one shot, the woman places her left hand on a support beam, but when the shot cuts, her hand is at her side. (01:26:55)
Continuity mistake: When Oppenheimer and Kitty are on the ranch, drinking from the flask in turns, he takes a sip. But from a different angle, his hand is suddenly down.
Continuity mistake: When Los Álamos is being built, Oppenheimer talks with a guy and draws four letters and circles on the board behind. Their styles change between takes.
Continuity mistake: When Oppenheimer comforts Jean, the position of his hand on her forehead keeps changing in every shot.
Continuity mistake: After Oppenheimer meets Jean, he takes the glass to his mouth, but from a different angle, it's lowered.
Continuity mistake: When Oppenheimer meets Jean, she is staring at him. Angle changes, and she is looking downward. Back to the first angle, and she stares at him again.
Answer: The short version is "no, not really". Much like in the film, the possibility was considered, a lot of calculations were done, and it was agreed by everyone privy to them that the chance was basically zero. Also like in the film: "what do you want from theory alone?" - it couldn't be guaranteed to be absolutely zero, but then the chance of almost anything happening is never absolutely zero. A 1946 report by three of the scientists stated: "whatever the temperature to which a section of the atmosphere may be heated, no self-propagating chain of nuclear reactions is likely to be started. The energy losses to radiation always overcompensate the gains due to the reactions."