(at around 1h 10 mins) The singer is shown standing with both hands on the microphone stand. When Hammer is sitting at the bar, during the same song, the singer is shown in a reflection playing a piano and not singing, though she is still heard singing.
When Hammer is brought to the beach house for the first time by the 2 thugs and is trying to escape the ensuing brief chase and fight is shown in alternating close ups and from distance. The shots from distance clearly show different actors, stand-ins for the thugs than those playing them in the close-ups and throughout the movie.
The goof items below may give away important plot points.
The "whatsit" is connected to Los Alamos, meaning that what was inside the box was nuclear. However, neither uranium nor plutonium would show a behavior similar to what is depicted in the movie, except for the heat generation and the radiation burns (Nick's wouldn't be fatal per se). The "screaming" and light manifestation is more typical of white phosphorus's reaction with air oxygen. Furthermore, opening the box would not trigger a nuclear explosion. Anyway, an explosion of the kind that ends the movie would contaminate a significant portion of California with radioactive material.
Near the beginning of the film, as Christina is being tortured by Dr. G. E. Soberin and a henchman, she continues to scream even after her legs stop moving, and she has apparently already died. In addition, at the end of the film, as Gabrielle opens "the great whatsit" box and is burned by the radioactive material inside, she utters the same identical scream long after she appears to have mostly gone up in flames.