Visible crew/equipment: When seen up close the aliens helmets have no openings. When the alien spaceship takes off outside the Belmont lab one of them is left inside. As he walks out the reflection of the window on the front of his helmet and the person in side can be seen in the sunlight. (00:54:20)
Deliberate mistake: After the aliens announce their intentions Dr. Marvin meets with Carol back at their hotel room. He tells her that she must take a flight alone back to Palm Springs and then leaves the room. In the end of the scene she picks up a copy of The Evening Star, which is an obvious prop as it has no date on it. (01:08:50)
Plot hole: After being denied permission to contact the aliens by himself, Dr. Marvin returns to his hotel and calls them up on the radio anyway and arranges to meet, despite not being allowed to leave the hotel. His wife says she overheard him say he's under orders not to leave and begs him to call someone instead: "Call Huglin". She shouldn't know who Huglin is because Huglin was only assigned to guard them as Marvin was being denied permission to contact the aliens.
Continuity mistake: At Carol's barbecue a soldier drives up in a jeep with a message for Dr. Marvin stating that they lost contact with rocket No. 11. Dr. Marvin holds the message and an envelope in his hand as they look up and see the rocket burning up in the atmosphere. He never puts the message back into the envelope but when he sits down the envelope is alone and the messages is gone. (00:13:50)