Factual error: There is not a snowball's chance of Howard becoming an astronaut. He suffers from cardiac arrhythmia, something about which he is completely open. "Transient" or not this is easily detectable by a simple electrocardiogram, which is a fundamental part of the many medical examinations a potential astronaut will have to pass. He wouldn't even be allowed to start basic training. Note also that during his basic training he shows signs of severe stress and trauma which would inevitably trigger a cardiac episode. Even if it didn't the fact that he was falling apart at the seams would have him removed from the programme for his own good.
Factual error: In the opening scene Addison and Pete are running on treadmills side by side. They are seen increasing their speeds to 8 mph and above. Addison even had hers to 10.1 mph yet they are both still talking, smiling, and laughing easily. 10 mph is a very fast speed for humans and they would not be able to laugh or even speak at those speeds. (00:02:10)
Factual error: When Chuck and Jill recover Guy LeFleur's hard drive containing the list of Fulcrum agents, General Beckman says that the flash drive is encrypted with a 512 bit AES cypher. She then goes on to state, "the computer is trying every possible key against the encrypted data, " i.e., a brute force hack. However, it would take the fastest supercomputer in the world longer than the existence of the known universe in order to crack even a 128 bit AES encryption (and a 512 bit AES encryption has the number of possible keys of a 128 bit AES encryption, raised to the fourth power). In a previous episode, Chuck refers to the computer in Castle as having a "30 teraflops" speed, which is far less than the current fastest supercomputer. General Beckman instead says it will take only hours or days. (00:26:10)
Factual error: At the pool party at the end of the episode, Asa Elliott is singing Gold by Spandau Ballet. Whilst he's singing, the shots change to different couples/families at the party. When Asa finishes the song, 5 minutes and 58 seconds have passed. The actual song is only 3 minutes 55 seconds.