Blair is referred to early in the movie as 1st Lt. Blair, but a few scenes later reports to the captain as Lt.(jg) Blair, the U.S. Navy's equivalent of First Lieutenant. Both are labeled as O2, technically the same rank level but different branches.
In the scene where Devereaux verifies Taggart rank on rapier console, the rapier communicates with the Tiger Claw to verify code punched in. The Tiger Claw was in Radiation field preventing any communications according to Rosie.
In Admiral Tolwyn's communication to Capt. Sansky, the Admiral's name is listed as "ADMIRAL TOWLYN." While this sort of thing could normally be chalked up to human error, spelling such a high ranking official's name wrong would probably subject a soldier to severe punishment.
On the Diligent, Taggart asks to see Blair's Pilgrim cross. When he looks at it he exposes a dagger-like blade. The blade looks longer than the cross it came out of.
When the Kilrathi are attacking Pegasus, they blast open both doors to the Command and Control room to enter. In the video on the drone seen by the Concordia Battle Group, only one door behind Admiral Wilson can be seen falling open.
While the Tigerclaw is hiding from the Kilrathi, the crew is cautioned to be very quiet. Sound does not travel through space, so the crew could blare rock music from every speaker at full volume and the Kilrathi wouldn't hear it even if their ship were five feet away.
When the Tiger Claw is hiding in an asteroid crater, the ship has shut down all active scanners and only has passive scanners enabled. However, when the sounding nukes are approaching, distinct sonar-like double pings can be heard, showing the incoming warhead getting closer. A double-ping would mean that an active signal is being sent from the Tiger Claw, bouncing off of the incoming warhead, and then returning to be detected.
While generally unrealistic, one flaw in the space-fighting is especially obvious. In several scenes the fighters can be seen starting from the Tiger's Claw very similar to modern jet-fighters starting off aircraft-carriers. This includes the slight drop shortly after leaving the ship. In space, and thus without gravity, the fighters should have started smoothly and in a straight line.
Machine guns would make no sound in outer space.
Sound cannot travel in the vacuum of space, yet you can hear Rosie's star fighter get pushed off the landing deck.
Early in the movie, during the Kilrathi attack on the Pegasus station, the computer screens repeatedly make reference to a "breech" of the station. The correct word is "breach." They mean completely different things.
When searching for the Kilrathi communication vessel, Blair announces "confirmed targets" on his radar when in fact, his AI system only relayed "possible hostile contacts".
At the beginning of the movie in command and control room when technician says "Command codes overwritten" camera is visible on the right.
There's no reference to Blair losing/not wearing his Pilgrim Cross, but he says he doesn't have it when he's asked to jump into Sol to warn the fleet. (In a scene that was deleted, he killed Admiral Wilson aboard the ConCom with the cross and left it with the body.)