The behavior of Renée Picard in the simulator and her emotional issues such as depression would make her totally unacceptable as a test pilot and most certainly unacceptable as an astronaut. Besides, one does not go straight from university to being a test pilot.
On Renée Picard's passport, "RÉPUBLIQUE FRANÇAISE" is misspelled as "RÉPUBLICIQUE FRANÇAISE". Furthermore, the use of diacritics is inconsistent.
Agnes fires the shotgun without pulling the hammer back to cock it.
Flipped shot: At 00:08:31: The Homeland Security writing on the rear and side of the bus is reversed.
When the gala security system is explained, the date of birth on Renée Picard's passport does not match the ID on the scanner readout and is written in the format month, day, year (American style) and not day, month, year, as would be expected in France. It can be seen that these numbers are supposed to match when Dr. Jurati's fake passport is scanned later on.
The French police officer radios back to dispatch that the Picard vineyard looks abandoned. Ignoring that he somehow couldn't see Agnes sleeping on a sofa very near to him, Picard and Agnes had started a fire in the fireplace earlier. Even if the fire had gone out, the smell of it and fresh ashes would be a sure sign that the house was not abandoned.
Seven tells Raffi that they can't use the transporter to beam Rios off the Homeland Security bus because such an act could severely affect the timeline, but then they help all of the other deportees escape, which in turn could severely affect the timeline.
Picard states that the Europa mission was a very important event in his timeline's history. Earlier, when attempting to ascertain the nature of the divergence in time, he is given the date of three days ahead. Yet somehow he does not make the connection between the date of the "very important mission" and the divergence in time.
Kore must live in a sterile environment because of a weakened immune system. In order to enter, her father must pass through a decontamination chamber. A decontamination chamber would kill any harmful foreign substances on his clothing or skin, but he would still have germs, bacteria, and/or viruses within his body that he could easily transfer to Kore simply by breathing the same air. He makes no effort to quell the spread of these microscopic organisms, such as wearing a mask or other protective clothing. This error is repeated every time Adam Soong enters his daughter's living quarters.
Q tells Dr. Soong that he will sit down at the booth in exactly 17 seconds. When Soong sits down, Q then says, "17 seconds, right on the tick." 22 seconds have elapsed since Q made his prediction.