Audio problem: When Oppenheimer is breaking up with Jean, he says, "We both know I'm not what you want, Jean." When the shot is focusing on Jean while saying the line, Oppenheimer's mouth isn't moving. (00:35:10)
Audio problem: When Frank is telling Robert about his engagement, there is a shot of Frank saying "I won't live my life afraid to make a mistake", which cuts to focus on Robert midway through the line. When the shot is on Robert, Frank's mouth cannot be seen moving during the line. (00:26:15)
Audio problem: Whilst Lewis is waiting to testify before the Senate for the first time, he says, "Are they really going to ask about it? That was years ago," to the Senate aide. Whilst saying, "It was years ago," the shot cuts to the Senate aide, where Lewis can be seen in the corner of the frame, and his mouth isn't moving. (00:02:15)
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."