In the bedroom scene where John Connor is complaining about having been moved to a small town, he is listening to the song "Pardon Me" by Incubus on his CD Player. The song is the intro to the scene, which is cut off when his headphones are removed. This breaks continuity because it is supposed to be September 1999, and the "Incubus" Album "Make Yourself," which the song was first featured on, did not come out until October of that year.
When Cromartie walks up to the bank he determines that the S.W.A.T. team is no threat as they lower their weapons at the sight of him. From his appearance it would be understandable that they would be taken aback, since none of them know what they are really looking at. This doesn't explain why a moment later they don't act to stop him when Cromartie smashes through the doors into the bank, as this is what they are trained to do.
In Terminator 2, John Connor is 10 years old, as we can see when the T-1000 looks up at the police car's computer. So the events in T-2 took place in 1995. As mentioned by John in this episode, 'that' happened 2 years ago, so this episode should be placed in 1997 instead of 1999.
When Sarah, John and Cameron go through the time vortex, they lose everything they were carrying - clothing, weaponry, and even bandages. Whilst Cameron's open wounds from battling Cromartie earlier in the episode are clearly visible, there is no sign of Sarah's gunshot wound to the shoulder.
In the opening sequence when Sarah and John get arrested, Sarah is shown being forced into the police car from the passenger side. It then cuts to clip of the policeman pushing Sarah's head down into the car from the driver's side. Finally, it cuts to shot from inside the car showing Sarah entering from the passenger side.
In the information Agent Ellison is editing, Sarah Connor's height is listed as 5'4" and her race is listed as "Caucasian", and the mental facility Sarah escaped from is incorrectly spelled "rescadaro". However when we switch to the Terminator's computer, the bulletin, which otherwise contains the exact same information, lists her as 5'5" and her race is "White". The mental facility now also matches that of Terminator 2 - "Pescadero".
In the scene of Agent Ellison first meeting Charlie Dixon a wall clock can be seen on the wall several times, albeit briefly. Look closely and you can see that the clock isn't working, as the second hand doesn't move.
When her fiancé presents the ring, Sarah says John is 15 years old, moments later the FBI computers shows 16 as John's age. Possible explanation: the FBI computers calculate John's age by the year of his birth, hence he's technically 16 years old, but his 16th birthday is sometime after August 24th, so actually he's still 15 years old.
The goof item below may give away important plot points.
The time jump is indicated on the machine as T+78892.31165. Assuming this value is in hours, the jump would be about eight hours less than exactly nine years. Unfortunately the actual jump is almost exactly eight years (from 1999 to 2007). (It may be argued that the number is given in a different unit, but this is highly unlikely. The unit would then be about 3200 seconds long.)