General Beckman tells Chuck that the government has spent three years and a lot of money to train him a spy. However, his spy training only lasted a few months in Prague (and he failed it). In the first couple of years, Chuck was simply used as the human Intersect and, in a few occasions, Beckman had no qualms about terminating "Project Bartowski" and having Chuck killed.
The US Air Force doesn't and wouldn't conduct an air strike within the US.
The Posse Comitatus Act of 1878, as amended, prohibits the use of the military including the air force in domestic law enforcement activities. This means that the military, including the Air Force, cannot be used to enforce domestic laws or conduct domestic operations, including air strikes, except in very limited circumstances such as when authorized by the President or Congress in response to a national emergency or during certain types of civil disturbances.
When Chuck locks Sarah in the Castle for her own safety, she notices that Casey is in Buy More and uses Morse Code to signal him. Casey having been stripped of his military rank would certainly have had his fingerprint access to the Castle revoked yet, in the next scene, he is able to get into the Castle and release Sarah.
Sarah says she doesn't feel the same way about Chuck and she won't go to Italy with him and instead will go to DC with Shaw because she thinks Chuck killed someone. This makes no sense considering Shaw has killed many people in past missions and if Sarah is turned off by that, she would have been turned off by Shaw too.
Chuck flashed his way into the Ring basement through the vending machine. Since this was a secret hideout, the information about the vending machine's code shouldn't even exist in the Intersect.
Brigadier General Beckman commits a number of uniform errors: 1) She wears her ribbons in the wrong order. She displays the Global War on Terror Expeditionary Medal and the Global War on Terror Sevice Medal at a lower order of precedence than the Kuwait Liberation Medal (Kingdom of Saudi Arabia) and the Kuwait Liberation Medal (Government of Kuwait). United States Military Awards are always given higher precedence than foreign military awards on any US Military uniform. She also wears the Humanitarian Service Medal ahead of her Global War on Terror Medals. This medal is of lower precedence than any of her campaign medals. 2) She wears her service jacket with the tab of the left epaulet over her collar. The tab is always tucked under the collar.